tenth international conference on soft computing applied in
Transkript
tenth international conference on soft computing applied in
EVROPEAN POLYTECHNIC INSTITUTE, Ltd. KUNOVICE PROCEEDINGS „TENTH INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS“ ICSC 2012 January 20, Kunovice, Česká republika Edited by: Prof. Ing. Imrich Rukovanský, CSc. Doc. Ing. Mirslav Mečár, CSc. Prof. Ing. Pavel Ošmera, CSc. Ing. Jaroslav Kavka Prepared for print by: Ing. Andrea Kubalová, DiS. Bc. Martin Tuček Printed by: © European Polytechnical Institute Kunovice, 2012 ISBN 978-80-7314-279-7 INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS ICSC 2012 Organized by THE EUROPEAN POLYTECHNIC INSTITUTE, KUNOVICE THE CZECH REPUBLIC Conference Chairman H. prof. Ing. Oldřich Kratochvíl, Ph.D., CSc., Dr.h.c., MBA rector Conference Co-Chairmen Prof. Ing. Imrich Rukovanský, CSc. Doc. Ing. Miroslav Mečár, CSc. INTERNATIONAL PROGRAMME COMMITEE O. Kratochvíl – Chairman (CZ) W. M. Baraňski (PL) K. Rais (CZ) M. Šeda (CZ) J. Baštinec (CZ) J. Brzobohatý (CZ) J. Diblík (CZ) P. Dostál (CZ) U. Chakraborthy (USA) M. Kubát (USA) P. Ošmera (CZ) J. Petrucha (CZ) I. Rukovanský (CZ) G. Vértesy (HU) I. Zelinka (CZ) A. M. Salem (ET) A. Borisov (LT) M. Wagenknecht (GE) Session 1: ICSC – Soft Computing a jeho uplatnění v managementu, marketingu a v moderních finančních systémech Session 2: ICSC – Soft Computing – tvorba moderních počítačových nástrojů pro optimalizaci procesů Opponency Board Doc. Wlodzimierz M. Baraňski, Wroclaw University of Technology, Wroclaw, PL Prof. Ing. Petr Dostál, CSc., Vysoké učení technické, Brno, ČR Doc. RNDr. Jaromír Baštinec, CSc., Vysoké učení technické, Brno, ČR CONTENTS ÚVODNÍ SLOVO ................................................................................................................................................. 7 PROPOSAL OF SIMULATION STUDIES FOR THE PURPOSES OF ARCHAEOLOGICAL PREDICTIVE MODEL........................................................................................................................................ 9 Stanislava Dermeková, Dalibor Bartoněk .......................................................................................................... 9 HISTORICAL MAPS IN GIS............................................................................................................................ 17 Dalibor Bartoněk, Stanislava Dermeková, Irena Opatřilová ............................................................................ 17 THE PREDICTION OF SALE TIME SERIES BY ARTIFICIAL NEURAL NETWORK ........................ 27 Petr Dostál, Oldřich Kratochvíl ........................................................................................................................ 27 VÝKON DATABÁZOVÝCH SYSTÉMOV NA HARDVÉROVÝCH PLATFORMÁCH .......................... 31 Juraj Ďuďák, Gabriel Gašpar, Michal Kebísek ................................................................................................ 31 DATA ANALYSIS & MODELING USING OPEN SOURCE SOFTWARE R ............................................ 37 Lukáš Falát ....................................................................................................................................................... 37 OPTIMISATION OF DECOMPOSITION STRATEGIES IN PARALLEL ALGORITHMS ................... 43 Ivan Hanuliak ................................................................................................................................................... 43 PERFORMANCE OPTIMIZATION OF BROADCAST COLLECTIVE OPERATION ON MULTICORE CLUSTER ............................................................................................................................................... 51 Hudik Martin .................................................................................................................................................... 51 PERFORMANCE MODELLING OF MATRIX PARALLEL ALGORITHMS.......................................... 57 Filip Janovič ..................................................................................................................................................... 57 MATHEMATIC EVALUATION OF ECOTOXICITY TESTING ............................................................... 65 Kateřina Kejvalová ........................................................................................................................................... 65 MANAGERIAL DECISION-MAKING: MEASURING AND MANIFESTATIONS OF RISKS .............. 75 Dusan Marcek .................................................................................................................................................. 75 TESTING OF TOPCON GRS-1 INSTRUMENT USING RTK METHOD .................................................. 81 Irena Opatřilová, Dalibor Bartoněk .................................................................................................................. 81 QUANTUM MODEL OF ATOMS ................................................................................................................... 89 Ošmera Pavel.................................................................................................................................................... 89 RBF NEURAL NETWORK APPLICATIONS USING JNNS SIMULATOR .............................................. 95 Jindřich Petrucha .............................................................................................................................................. 95 OPTIMIZATION OF THE THROUGHPUT OF COMPUTER NETWORK ........................................... 101 Imrich Rukovansky ........................................................................................................................................ 101 MINISATION OF COMPLEXLOGICAL FUNCTIONS ............................................................................. 109 Miloš Šeda ...................................................................................................................................................... 109 PERFORMANCE MODELLING OF MULTIPROCESSOR PARALLEL SYSTEMS ............................ 117 Dan Slovaček.................................................................................................................................................. 117 DESIGN AND CONSTRUCTION OF EXPERT SYSTEM FOR ANALYSIS OF RECREATION ATTRACTIVENESS ........................................................................................................................................ 123 Yaroslav Vyklyuk, Olga Artemenko .............................................................................................................. 123 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 5 PRINCÍPY OPRIMALIZÁCIE NAVRHOVANIA ELEKTROMECHANICKÝCH AKČNÝCH ČLENOV ............................................................................................................................................................................ 127 Juraj Wagner .................................................................................................................................................. 127 JMENNÝ REJSTŘÍK ....................................................................................................................................... 137 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 6 ÚVODNÍ SLOVO Konference „ICSC – International konference on Soft Computing Applied in Computer and Economic Environments“ proběhla sice již po desáté, ale poprvé ve virtuální technologii. Účastníci konference přišli z 5 univerzit a výzkumných institucí. Recenzované příspěvky v počtu 18 se věnovaly vývoji v oblasti teoretických disciplín (Optimisation of Decomposition Strategie in paralel Algorithms atd.), především však aplikovanému výzkumu v oblasti aplikované informatiky a elektroniky. Cílem konference bylo umožnit akademickým pracovníkům zveřejnit výstupy jejich vědecké práce a podrobit je veřejnému posouzení. Ve sborníku se nachází jen ty příspěvky, které prošly recenzním řízením. Nedoporučené příspěvky mohou autoři dopracovat a navrhnout v květnové konferenci k novému hodnocení. Sborník příspěvků bude odeslán autorům a jako povinná odevzdávka do univerzitních knihoven v ČR. Je mně ctí poděkovat nejen všem akademickým pracovníků, recenzentům za jejich práci, ale také vědeckému výboru konference a organizačnímu výboru konference za vynikající práci. Oldřich Kratochvíl Ing. ,h. prof., Ph.D., CSc., Dr.h.c., MBA rektor EPI, s.r.o. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 7 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 8 PROPOSAL OF SIMULATION STUDIES FOR THE PURPOSES OF ARCHAEOLOGICAL PREDICTIVE MODEL Stanislava Dermeková1, Dalibor Bartoněk2 1 University of Technology, Faculty of Civil Engineering, Institute of Geodesy 2 Evropský polytechnický institut, s.r.o. Kunovice Abstract: The process of simulation model generally represents a reconstruction of its way and prediction of the possible existence of phenomena reflecting objects investigation. The subject of modeling and simulation is to study objects that may already exist in reality or it could exist. The paper deals with the existence of objects in a time long past, which can be described by the simulation prediction model. The core modeling spatial phenomena prediction model through simulation process is to conduct not only spatial analysis of archaeological data, but also the use of instruments examining the characteristics of landscape elements and factors affecting the incidence of long-past history. Keywords: Simulation model, GIS, archaeological predictive model INTRODUCTION The process of simulation model building generally represents a reconstruction and its way a prediction of the possible existence of phenomena reflecting objects investigation. The subject of modeling and simulation is to study objects that already exist in reality or it could be. The paper deals with the existence of objects in a time long past which can be described by the simulation model prediction. The core of the modeling of spatial phenomena prediction model through simulation process is to conduct not only spatial analysis of archaeological data, but also the use of tools for examining the characteristics of landscape elements and factors affecting the occurrence of long-past history. Results of simulation study will be complete simulation model for purposes of archaeological prediction. The life cycle of the simulation process is composed of two stages: design and development of simulation model and experimentation with the model. The paper also deals with the various individual stages of the simulation studies in archaeological predictive models. Through simulation as a research technique, whose primary objective is the substitution of simulator certain studying dynamic system. It will be predicted the abstraction of object model solved the archaeological site. Using the simulator is experimented objectives for obtaining information on the original scheme. From the results of simulation studies can reconstruct the appearance of the remains of human activity from ancient times using 3D modeling and visualization. 1. MODELING AND SIMULATION The subject of modeling and simulation is the study of the objects that may already exist in reality or it could be. If we deal with the existence of objects in a time long past, can be described by the simulation predictive model. In examining these objects is often not possible to describe the object rationally in all its complexity therefore the description of the investigated object is applied an abstraction (some aspects of objects that are not important in solving the problem, are neglected and insignificant characteristics are described in a way that leads to the manageable solution to the problem). That can’t accurately predict the location extinct by describing the object. On objects (parameters) to be studied is made in the modeling system definition, and one object can be defined in different systems depending on the different angle of view under which the object is observed in various fields of human activity. A different point of view is arising from the existence of parameters that are influenced by various factors depending on the variables. The system, in which disregards the importance of the passing of time, called a static system. Experiments in simulation of static system for archaeological predictive model (APM) would represent a simple analysis only connected with the rights geological, climatic and landscape character of the studied area. System in which we are considering the passing of time called a dynamic system. Time instants of a dynamic system are identified as well as for the abstraction. Experiments in simulation study of dynamic systems offer in predicting a wide range of analysis that can be combined in different options. [2] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 9 In a dynamic system in the modeling process and simulation is considered that the system consists of certain elements (entities / elements). We distinguish between permanent and temporal elements. Permanent elements occur in the system throughout its existence. The permanent elements in the archaeological prediction modeling can sort elements: land use (landscape features - height, slope, exposure to the field), geological and climatic nature of the territory, and others. Temporal elements can entry into the system and leaving it again. We consider the temporal elements in APM: a factor of appropriate environmental protection, economic factor, factor of minimum effort, defensive factor, cult factor, and other socioeconomic factors. 1.1 THE DEPENDENCE OF OBJECTS IN THE MODEL OF SIMULATION After defining the system to the objects of the investigation are clearly insignificant properties on objects that are subjected to closer scrutiny. In our case the objects of the investigation will be a location of the potential archaeological site in a particular historical period. There are elements that don’t enter directly into the purpose of the investigation but it is necessary to consider their existence because of respect to the examinee. Correlation of elements is very important. The interdependence of different variables directs the operation of prediction in historical documents. It can be used interaction modeling in the simulation process where each comparing factors. These factors are dependent on variables. Interaction modeling is a strong correlation between the individual elements that can be identified as important factors influencing on the prediction of a particular place. Important factors occurring in the predictive model include the land use factor, the cult factor, economic factors, social factors (socioeconomic factors), a defensive factor, factor in the minimum effort, and others. 1.2 THE PROCESS OF MODEL BUILDING The essence of modeling is a substitute of the investigated system of the model which aim is to get information through experiments with model on the original modeling system. Simulation is a research technique. The essence of simulation is to substitute of the considered a dynamic system (a system in which we are considering the passing of time) with the simulator. By experimenting with the simulator is to obtain information about the original investigation system. Run the simulation program can be seen as carrying out a sequence of activities in the order in which they perform their corresponding actions in simulation systems. [2]. Activities (processes) of the model can be divided according to nature: Discrete phenomena - the building of APM is preferable to consider discrete activities that change state only at the time of its completion and their time existence is understood only as a single element set of real numbers (the time by which the planned completion activities). Individual objects can be divided into sections on the coordinates X, Y. Its have limits which are spatially defined. There are mostly vector data model. Continuous phenomena – they cover continuously the whole territory, the phenomenon can not be stopped (to find the exact limit). We determine the value of the phenomenon in the spot X, Y. It is a raster data model usually. The values of entity attribute change only at discrete time moments in APM. The reason is clear evaluation of the results in parts of interaction analysis of the process simulation. Clarity is very important in archaeological prediction because in this project is still considered only place which existence has long since disappeared. 1.3 ARCHAEOLOGICAL PREDICTIVE MODELING The process of building of the archaeological predictive models is a specific approach and solutions. APM is a tool that should simplify the archaeological research in the field of systems of settlement and land use in the past. APM is a certain degree of accuracy the probable location of parts of the country which was previously used and which can now predict the occurrence of archaeological sites. The problem of archaeological predicts is solved by experiment sites (areas, packing areas), which typically are not usually randomly distributed, but occur with respect to the geographical environment and settlement organization. The starting point of a correct archaeological predictive model is to find the interdependence and carefully selected set of factors in the input documents that affect the distribution of archaeological sites. Correct correlation of the setting parameters creates the possibility of identifying sites in the country in which they are to find archaeological sites with high probability. [4], [6] Summarize of the input documents and their evaluation in the initial phase of APM is a certain amount of attention and knowledge of archeology, Fig. 1. The expert analysis addresses the first correctness of data entry documents where is created a database of all documents (maps and graphic materials, literary sources, material ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 10 artifacts). Emphasis will be placed on a database of historical documents that will be used to analyze the influence of time factor. The time factor affects on the every part of the solution prediction model. Any analysis, each base, each output is affected by factors of time because is needed the expertise of historical objects. These objects are changing in appearance and properties from the time. It is desirable to input documents consult with experts. Interaction of experts is very important to address the process of model building. It represents the experience and expertise in terms of make informed people from the fields of archeology who determined the exact rules and parameters for prediction of term solution. Of the selected documents are creating a simulation model to base GIS. In the process of creation is also using all the tools and modules in GIS thematic layers. Model Builder applications, map algebra, 3D Analyst, Spatial Analyst create a full prediction model which can be handled in different ways. [5] Fig. 1 Scheme of different parts of archaeological predictive model Expert system in predictive models is using settings of parameter that will be more precise each thematic layer. Parameters that affect the location of the archaeological site are: altitude, slope of terrain, distance from watercourse, communication, religion and others. Outside the spatial parameters can be considered a way of behavior of people in the past. Factors that affect the way the behavior of people are as follows: cult factor, economic factor, the factor of environmental suitability, defensive factor, factor minimum effort and others, Fig. 2. The actual implementation of the analysis in the GIS occurs to simulate the presence of archaeological sites after the setting of the parameters of the model arises. Spatial analysis is combined and used multi-criteria, interaction, hydrological modeling, model of the petrology and others. All created spatial analysis should be subjected to an influence analysis of the time factor which is used to create a database of historical documents and there is mutual comparison of statistical and graphical output of results in different time periods. The outputs of predictive model are the visualization of sites of archaeological locations in relation to their probability. The formulation of outputs is specific. It depends on the solved at a site, the terrain and the presentation of appropriate sites for archaeologists. [7] Fig. 2 Expert system ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 11 2 SIMULATION STUDY The core of the whole project is the creation of simulation studies which will result in a complete simulation model. The whole process of simulation is implemented in ArcGIS software. Basic diagram of connection is shown in Fig. 3 where is presented each of the step in the modeling. In the first stage of the creating is preprocessing which is usually the largest component of the process. Continuously builds an important part of the simulation and its associated archaeological prediction. In this stage are used different types of models. For purposes of archaeological prediction applies modeling of multi-criteria, interaction modeling, hydrologic models, erosion models and others. Reciprocal correlation model eliminates the uncertainty of the location of potential archaeological sites. The final part is the postprocessing which connects the individual outputs of each simulation model. The life cycle of the simulation process (studies) consists of 2 stages: design and simulation model development and experimentation with the model. The procedure of making is described at each step of its implementation. [1] 2.1 PHASE 1. – DESIGN AND DEVELOPMENT OF SIMULATION MODEL 2.1.1 INDICATION OF THE OBJECTS EXAMINATION AND THE ISSUE OF STYLIZATION Creation of archaeological predictive model using the simulation method is a process where objects are destroyed examining medieval settlements and their prediction. Defined object of investigation is experimented on the research methods of simulation. Prediction of the location of the settlement will be at the core of the project simulation model. The suitability of the site would result from different combinations of spatial analysis undertaken, which will describe the sub-objects examination. 2.1.2 THE SETTING AIM OF PROJECT AND TIME SCHEDULE The aim of project is using of prediction of defunct areas and their interaction modeling by spatial analysis in ArcGIS software. Time schedule of the project requires extensive time reserve for the procurement of necessary documentation, documentation and input data for progressive graphics verification. Part of the definition of reserves is the control of technical and substantive correctness of input data to avoid mistaken and negative influences. The solution for spatial analysis requires a large proportion of the total schedule of the simulation model. 2.1.3 DETERMINATION OF THE SYSTEM On the object of examination is applied an abstraction. Specify the simulated system (the original). It is needed to accurately determine the correctness of input data and their thematic distribution. Suitability of the material is achieving the objectives and solves problems without the need for further analysis and experiments. 2.1.4 CONCEPTUAL MODEL An important part of life simulation model is the choice of appropriate methodology (concepts). In the election play an important role in the methodological procedures that will gradually narrow range of solutions to the problem resulting "clear" verification. The choice of types of interaction modeling will be will be a key for the further course of archaeological predictive models. 2.1.5 COLLECTION AND ANALYSIS OF DATA CORRECTNESS Data collection and their analysis take place parallel with the formation of the conceptual model. The process of the data collection process is the most important part of the project. Phase of search suitable materials requires considerable attention because of streamlining downstream spatial analysis. The input data are important for decision-making rules relating to the issue of conflict resolution. Search for documents in them include communication with the various institutions which represents the risk of negative feedback. It is therefore important to ensure the correctness of received documents to prevent false information at a lower number of input data. The process of data collection and analysis are dependent on the requirements which have been set in the conceptual model solutions. The concept of the model will set the direction of its own collection of input documents. 2.1.6 DEVELOPMENT OF SIMULATION MODEL In ArcGIS software will be designed and implemented the appropriate data structures. It is necessary to determine the main parameters of which will be based, and which will form the skeleton of model. Enter the following parameters will be important for directing operation of the simulation model. It should be available to ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 12 use simulation tools to the ArcGIS software offers in the archaeological predictive models. Appropriate tools can be the 3D Analyst, Spatial Analyst, Map Algebra offers other components ArcGIS software. An interaction between these instruments is very important. 2.1.7 VERIFICATION OF SIMULATION MODEL Verification of functional correctness of the simulation model represents the first phase of the control components interdependencies that were initially established in the conceptual model. Different methods for testing the functionality of input and interaction of sub-documents have for verification of archaeological predictive model. It will be applied the main methods of analysis using spatial interaction modeling, assessment of multi-criteria, land use analysis and others. Testing the processes interaction requires a great deal of knowledge to tackle (study of the historical sources, archaeological documentation, documents representing landscape features, geological and climatic characteristics and other countries). Deficiencies found during verification lead to legal intervention in the process of design and production simulation model. 2.1.8 VALIDATION OF SIMULATION MODEL Validation is testing of the veracity of behavioral simulation model and the correctness of the result of processes of spatial analysis. Implementation of validation in itself includes a variety of methods [2]: Method of compare with reality – using comparative methods of the dealing concept of using statistical methods. It is using processed archaeological data of existing archaeological sites, the State Archaeological Database System, exploring the surface collections solutions to existing sites. Compare with other models – validation that will be created to compare each model with a fundamentally different structure model. Examples include models using modeling of multi-criteria on the base of fuzzy logic, neural networks, interaction modeling using hydrological analysis, etc. Empirical method – using expert assessment by an independent expert. Consultation various parts of the concept and created a simulation model with knowledgeable experts in the field of archeology. Negative results of the validation may lead to structural changes in the conceptual phase of the simulation model to review the correctness of input and concise treasures to repeated changes stylistics issues. 2.2 PHASE 2. – EXPERIMENTING WITH THE SIMULATION MODEL 2.2.1 THE SIMULATION TEST PLAN The plan attempt depends on the frequency and accuracy of input documents. The proposed plan may be modified based on the results progressively obtained. It is necessary to consider the impact of the time factor of historical documents and their relation to the contemporary world.. 2.2.2 IMPLEMENTATION OF THE PLAN AND PROCESS ANALYSIS Using GIS software includes itself in the mathematical combination of spatial data to create derived data which may provide new insights into natural phenomena and anthropomorphic. These can be further used in the geological models for predicting the suitability of reverse land for agriculture or predicting erosion potential or the potential deployment models in archaeological sites. To create the simulation model that would allow defining, analyzing and evaluating residential development followed in the past, the selected area on the basis of criteria determined from revised and localized archaeological data. Mathematics - simulation model for predicting in archeology works based on the known archaeological patterns, several calculations were carried out by the facts. The core of the process simulation model is a description and analysis of how the behavior of people - simulating the actual behavior. Between the individual analyses I try to model the social dynamics of the population and predict the possible occurrence of a real historical settlement. The model uses a deliberately thought processes from individual to the general, the models, patterns, concepts of factors that do not only features of the landscape, but also focuses on the patterns and effects resulting from the spatial position and cross-functional compatibility of memory space. Created model simulates the dynamics of changes in functional use of space in this area by combining the results of the analysis. Efforts to understand and correct evaluation of often very complex behavior of a spatial system is usually difficult because of the resulting documents, which represent an informed decision and simulation caused by the influence of individual factors in the area. For modeling purposes as a representation of the real (historical) world the wide range of alternative applications Model Builder can be used. The ArcGIS software can create models of "localization" process model (variables, parameters and their influence tackle) model description (description of issues examined). The benefits of the Model Builder application, is creating its own sequence of functions and their parameterization (modification of ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 13 function parameters, respectively. Instruments), modification of storage functions, scripting languages and others. The iteration of the individual process creates detailed and final output in spatial analysis in the application. 2.2.3 DETERMINATION OF THE FEASIBILITY OF ALTERNATIVE EXPERIMENTAL (FEEDBACK) When evaluating the specific factors of historical events is not enough just to work with absolute variables that reflect the modeled variable without reference to other modeled quantity, time period and area. It is necessary to have the values of these variables in other situations and compare their relative manner proportional method. Comparison can be done by either absolute difference, comparative index (time index, geographic index, and mixed material index). Confrontation of the output analyses with archaeological documents and papers state the possibility for the alternative experiments because of the low reliability of the results for the final prediction of perished areas. The process of deciding on the appropriateness of the models and their combination for predicting the archaeological site potential requires a great deal of knowledge about the issue as well as discussions with skilled and knowledgeable professionals. Although the location of archaeological prediction may not always be complete, ambiguity and uncertainty of determining the place can be alternate with other spatial analysis of multi-criteria modeling. Therefore it is important to confront your knowledge of simulation modeling with experts to determine the alternative solutions. 2.2.4 DOCUMENTATION OF RESULTS Graphic outputs of simulation model results are heterogeneous. For the purposes of archaeological prediction models are useful mapping outputs with related factors which affect the decision-making on the suitability of sites of potential archaeological sites. Combining the resulted layers of analysis and graphical presentation is an excellent instrument for intuitive visualization of the possibility of settlement. Through simulation the archeological site can be reconstructed in the form of 3D models directly applied to the solved area. For example: making a real contemporary look of the village by using simulations according to the available historical documents helps archaeologists in the visual orientation of the territory. 3D model of the ancient settlements is a part of a comprehensive analysis of the simulation study. Its combination with the spatial analysis moves simulation process to concrete results with decreasing percentage of localization uncertainty of potential archaeological sites. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 14 Fig. 3 The life cycle of the simulation process ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 15 3 CONCLUSION The paper deals with the existence of objects in a time long past, which can be described by the simulation model prediction. The core modeling spatial phenomena prediction model through simulation process is to conduct spatial analysis of archaeological data only, but also the use of instruments examining the characteristics of landscape elements and factors affecting the incidence of long-past history. The simulation model is linked to ArcGIS software environment that offers a method of simulation by spatial modeling. In the spatial analysis are considered factors that affect the suitability of the location of potential archaeological sites. In the simulation study, which consists of two phases, the experiment phase is in various combinations of post processing analysis of the results. The simulation of the archaeological prediction provides us with the abstraction object model solved for the archaeological site. Simulation in the GIS environment is a suitable tool for visual representation of dependencies of the variables and factors modeled site. Through the simulation archeological site can be reconstructed in the form of 3D models and visualization applied directly to the solved area. Combining 3D models with spatial analysis reduces the percentage of localization uncertainty of potential archaeological site, for better visual connection of the location with reality and its possibilities for the existence of historical settlements. LITERATURE [1] KAVIČKA, A. Modelování a simulace. Pardubice : Electronic lectures of the course of Modelling and Simulation. 2005. [2] KŘIVÝ, I.; KINDLER, E. Simulace a modelování. Ostrava : Textbooks, University of Ostrava, 2001. [3] CENDELÍN, J.; KINDLER, E. Simulace a modelování. Plzeň : Publishing Centre, UWB, Textbooks UWB Plzeň, 1993. 230 s. [4] GOLÁŇ, J. Archeologické predikativní modelování pomocí geografických informačních systémů – na příkladu území jihovýchodní Moravy, Brno : PhD Thesis, Masaryk University, Faculty of Science, Department of Geography. 2003. [5] MACHÁČEK, J. Počítačová podpora v archeologii 2. Brno – Praha – Plzeň : Department of Archaeology and Museology, MU Brno, Institute of Archaeology in Prague, Department of Archaeology ZU Plzeň, 2008. [6] NEÚSTUPNÝ, E. Předvídání minulosti, Technical magazine 11. 58-60 s. [7] KUNA, M. Geografický informační systém a výzkum pravěké sídelní struktury. In: Macháček, J (ed.), Počítačová podpora v archeologii, Brno : Masaryk University, 1997. 173-194 s. ADRESS: Ing. Stanislava Dermeková University of Technology, Faculty of Civil Engineering, Institute of Geodesy, Veveří 95 602 00 Brno, Czech Republic [email protected] Assoc. prof. Dalibor Bartoněk EPI Kunovice Osvobození 699, 686 04 Kunovice, Czech Republic, phone: +420-605912767 [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 16 HISTORICAL MAPS IN GIS Dalibor Bartoněk2, Stanislava Dermeková1, Irena Opatřilová1 1 University of Technology, Faculty of Civil Engineering, Institute of Geodesy 2 Evropský polytechnický institut, s.r.o. Kunovice Abstract: The contribution deals with the usage of old maps in GIS for urban re-development. As a model area the historical centre of Brno (Czech Republic) city including st. Peter-Paul’s cathedral and Špilberk castle were selected. On the basis of historical maps, plans and documents the main temporal points of urban development were established. The goal of this project was to attempt to establish urban re-development in these temporal points. The project analysis was made together with the cooperation of the experts of the middle age archaeology branch. Final output is a GIS project in ARC/INFO created with the geo-database, which contains all temporary levels of map sheets, significant geographical objects with the attribute data and historical and current time photos of the interested objects. In ARC/INFO system also 3D model of Špilberk castle have been created. Keywords: old maps, city plans, GIS, historical data warehouse, 3D model. 1. INTRODUCTION Historic buildings or conservation area has undergone during its history many changes. They changed not only the appearance of the objects but also their style, layout or functionality. The aim of this project was to determine the method of reconstruction of historic buildings on the basis of contemporary materials (documents, reports, maps, photographs, etc.) and using GIS to determine their location or appearance at some stage of their development (Procházka, 2007, 2009, Štěpánková, 2009). In the region of interest were selected historical centre of Brno and Špilberk castle. Brno is the second largest city in the Czech Republic with more than 400 000 inhabitants. It is the administrative centre of South Moravia, and its historic district is a separate part of Brno - the city. The entire project was run in several major phases – see Fig. 1: 1) Collection of historical materials relating to the area of interest, 2) Assessment of the materials and consultation with experts in the field of history, 3) Preparing and selecting the appropriate program; processing, 4) Data processing and analysis of appropriate software, identifying the main stages in which there were significant changes in the region, creation of geo-database, 5) Creation and presentation of outputs. Each phase of solutions is described in subsequent chapters. Materials collection Evaluation of materials Data preparation, choice of software Consultation with experts - historians Analysis, processing Outputs, presentation s Creation of geo-database Figure 1. Development of the project 2 HISTORICAL DATA COLLECTION AND EVALUATION This phase was the most difficult of all (Hitchcock 1996). Although the center of Brno has a rich history, historical material has been preserved relatively little. The paradox is that most of the preserved historical documents were located outside the city of Brno, even outside the Czech Republic. In fact, some of the organizations visited as Museum of Brno city, Archive of Brno, Moravian provincial archive, National office for ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 17 preservation of historical monuments in Brno, bishopric of Brno have some materials but the quality of its was in many cases insufficient. The most valuable items were found in the Military Archives in Vienna. It concerns the collection of 21 plans since 1658 – 1819, 5 profile sheets and 3 sheets of construction plans. All above mentioned materials were purchased by Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology for the needs of this project. Current map materials necessary for the reconstruction were provided by Facility management of Brno city and Czech Office for Surveying and Cadastre (Charvát et all, 2007). To the oldest and the most valuable exemplary belong de Rochepien’s plan of Brno city of 1749 and the plan of 1754 - see Fig. 2. Overview of all collected historical materials is given in Table No 1. Collected data were evaluated with the help of experts from the field history and adapted for further processing. The collected materials collected occurred to be insufficient for processing. Above all it was necessary to look up and determine appropriate identical points for geo-referencing of old maps. Further it was necessary to verify current map material and compare them with a reality. For these reasons the collected data were completed with direct geodetic measurement in field (Pundt 2002, Vivoni 2004). The actual selection of suitable materials for reconstruction was consulted with experts at Middle age archaeology from Brno Museum. A basic document for a choice of appropriate elements and identical points for reconstruction was present cadastral map of a given locality. This map contained objects which can be divided into 2 categories: 1) Preserved parts of an object of late 18th century. 2) Objects with small construction works which cannot influence identification with old maps and plans (facades adaptations, building reconstruction on an original object etc.). Data source (company) Military Archive Vienna, Austria Archive of Brno city, Czech Republic Museum of Brno city, Czech Republic Archaia ltd., Czech Republic ELGEO ltd., CZ. Facility management of Brno city, Czech Republic Czech Office for Surveying and Cadastre Geodis Ltd., Brno Date 1658 - 1783 Number of sheets 29 Content Format 1720 – 1944 10 Plans of Špilberk castle and Brno city Plans, sketch of Brno city A0 – A1, raster, TIFF, 200 dpi A3, raster, JPEG 1749 - 1984 4 Plans in scale 1:1000 A3, raster, JPEG, TIFF, B/W DGN, DWG 1997 - 2004 3 2006 2006 2 1 2002 4 Plans of Špilberk fortification Digital cadastral map Building structure investigation of Špilberk fortification Fundamental Base of Geographic Data (3D) Raster CIT, vector SHP 2003 2 Ortho-photo 20 cm/pixel Geo-TIFF, JPEG DGN Raster, JPEG Table 1. Overview of all collected historical materials Above mentioned objects contained localities for placement of reference points for geo-referencing of old map documents. Other necessary identical points were obtained by geodetic surveying of south-west bastion of the castle Špilberk which was newly reconstructed in the year 2002 in the frame of archaeological research. These points are the most accurate (both in history and topography). On the contrary the historical maps and plans have the lowest quality which is influenced by these factors: The ravages of time, causes fading of drawing which results in losing a part of a map. Precision of scanning in case, the map consists of several (in many cases damaged) parts. The exact dimension of map frame and field are unknown. Method of geodetic measurement and its accuracy are unknown. Disunited attribute style of drawing of maps and plans (various line styles and weights). Therefore with transformation (geo-referencing) the accuracy was not determined and the whole process is only to a certain extent informative, but the only available one. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 18 Figure 2. Plan of Brno city from 1754 year Geo-referencing of historical maps was based on affine transformation according this equation: x q x cos y q sin x where q y sin( ) x tx q y cos( ) y ty (1) tx, ty is shift in the x, y axis, qx, qy is scale factor in the x, y axis, is angle of rotation, is coefficient of non-orthogonality of both axis 3 DATA PREPARATION AND PROCESSING For the project was selected by ESRI ArcGIS software. Before entering into ArcGIS some files had to be adjusted. Raster data was preprocessed with Adobe Photoshop (cropping, downsizing, conversion, etc.), vector data has been adjusted in MicroStation V8. Upon entering into the system ArcGIS had to be some layers georeferencing using identical points. In many cases, especially in historical maps, it was very difficult, because many elements of the past disappear. For the whole project was used S-JTSK system (Datum of Uniform Trigonometric Cadastral Network in the Czech Republic). All altitude dimensions were calculated into altimetry system Bpv (Baltic Vertical Datum after Adjustment). There were successively inserted into the system or a newly created 172 layers, which were grouped into 23 categories. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 19 From institutions or private entities have taken these layers: Historical maps, Ortho-photo maps, Geological map, ZABAGED (Fundamental Base of Geographic Data in the Czech Republic) – contour lines and topography, State map of Brno city in the scale 1:5000, Utilities map of Brno city Zoning plan of Brno city Current cadastral maps of Brno municipality Based on an analysis of existing layers were determined four periods in which were the most important urban changes, namely: 1750 – 1815 1816 – 1880 1881 – 1945 1946 – 2010 These new layers have been created further categories or layers: Municipality fortification, Situation in 1890, Housing development in four above mentioned periods, Historical sightseeing tour in 1750 and 1890 – see fig. 4 (Štěpánková, 2009), Digital terrain model with layers: TIN, aspect, slope, hillshade, view, TIN-grid – see Figure 8, Further were created followed special layers: Layer for WMS (Web Map Services) Layers of significant historical objects: st. Peter’s and Pauls’ cathedral, st. James church and German house, Graph of selected profiles of Špilberk hill, Group layers of reconstruction of Špilberk castle. For all newly created layers geo-database has been designed - see Figure 3 (Bartoněk et all, 2009). As a special part of the project was create a topography and altimetry reconstruction of the castle Špilberk. Based on historical and current maps was created 3D model of Špilberk castle during the Baroque period - see Figure 9 (Procházka, 2009). ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 20 Figure 3 Geo-database of historical objects 4 RESULTS AND OUTPUTS The main results of the project are: Collection of historical and contemporary material (map, documents, photographs and reports) of the selected location, Classification of the material, determine the main stages of construction work - see Figure 6, Create new layers that show major changes in selected buildings, Creation of a common geo-database of historic buildings, Connection to the WMS services, where each user can work on-line with the selected map data, A special coating on the important historical places of Brno (st. Peter and Pauls’ cathedral, st. James church and German house), Creation of GIS analysis in the locality - 3D Model, profiles, Complex process of reconstruction of the castle Špilberk in both 2D and 3D model. All major results are presented in Figure 4 to 9. Figure 4 shows the main phase of structural changes in the centre of Brno. There is marked historical guided tour in 1750 with outstanding stops. In Figure 5 you can see important milestones in the development of the St. Peter’s and Paul’s cathedral, based on old maps. Fig. 6 shows the historical centre of Brno in 1750 and Fig. 7 the same site in 1890. On both figures it is clear what significant changes have taken place during the 140 years. Relatively stable are church buildings and squares, big changes can be observed in transport infrastructure (rail, tram). Another figure 8 presents a 3D model of representative sites created in the 3D Analyst module in ArcGIS. Elevations of the legend are given in altimetry system Bpv (Baltic Vertical Datum after Adjustment). ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 21 Figure 4. Housing development and historical sightseeing tour in Brno The last figure represents the result of reconstruction of the castle Špilberk. This reconstruction in 3D has 2 phases (Pundt et all 2000): 1) The creation of Digital Terrain Model (DTM) of Špilberk hill – see previous Figure 8. 2) 3D model of historical reconstruction of Špilberk castle and its fortification – see Figure 9. For making DMT these materials have been used: A plan of Špilberk castle of 1984 borrowed from Brno Museum in the scale 1:1000. The plan contained contour lines with the interval 1 – 0,5 m which have been digitalized. Altimetry of Špilberk in ZABAGED system (Fundamental Base of Geographic Data) – see table 1. For 3D model of historical reconstruction of Špilberk castle and its fortification these materials have been used: Plan of 1749 by Pierre Philippe do Beichade de Rochepine containing 15 dimensioned sections. Plan of 1759 with 2 sections missing in the previous plan. Plan of 1809 showing the fortress damaged in the period of Napoleonic wars. 4 map sheets of 1917 containing detailed drawing of building adaptation in the years 1840 – 1880 including altimetry spots dimensioned heights of terrain and fortification. Contour lines ZABAGED (Fundamental Base of Geographic Data) in the locality. Geo-database of topography map created in a previous phase of the project. Current digital cadastral map of Brno centre. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 22 Figure 5. Significant re-building stages of st. Peter –Paul’s cathedral Figure 6. Historical centre of Brno city in 1750 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 23 Figure 7. Historical centre of Brno city in 1890 Figure 8. TIN model of historical centre of Brno city ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 24 Figure 9. Extent of Špilberk fortification (3D model) 5 CONCLUSIONS The goal of the project was documenting the historical development and changes in core of the housing city, creation of a functioning system of historical database, serving a special interest group of users. This process was done on the basis of maps imported into the ArcGIS program. Furthermore, it was also working with information obtained from literature. Some materials (especially historical maps) did not meet the required accuracy, therefore, had to be supplemented by direct measurement in field. Created project allows comparison the development of urban historical core of Brno in various stages of the Middle Ages to the present. Layers contain the most important of all elements ranked classified according to purpose, style and time. Further was created the fly over the terrain by module ArcScene. The entire project was exported into a format PMF (Publish Map Format), which can be viewed by AcrReader. This application enables users work with all layers without license (free ware). The project was completed WMS capabilities, which allows the sharing of geographic information in the form of raster maps on the Internet. Allows you to connect to the workflow software (GIS, CAD) geographical data (maps, satellite images, ortho-photo, etc.) stored on other servers, in different formats (*.jpg, *.tif, *.png). Showing thematic geographic information (layer), or composite map (overlay multiple layers). This data is already related to a given coordinate system, which allows us to their correct interpretation. Another contribution of this project is a creation of 3D model today non-existing baroque fortification of Špilberk castle. It will be historically the first 3D digital model of the citadel taking original shape the one the second half of 18th century. I believe the results of historical reconstruction of Špilberk castle and its surroundings will become a valuable contribution not only for institutes and people working in the field of medieval archaeology, but it will also draw attention of general public. The project is not completely closed, maps are prepared and depends only on the ideas of more effective treatment and complete, because each area, the building has a special history, characteristics that can be further described. REFERENCES [1] ŠTĚPÁNKOVÁ, A. 2009. Urban re-development of historical centre of Brno city. Diploma thesis, Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, 55 pp (in Czech). [2] PROCHÁZKA, T. 2007. Planimetric component of a map reconstruction of historical fortification of Špilberk castle. Bachelor thesis, Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, 29 pp (in Czech). ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 25 [3] [4] [5] [6] [7] [8] [9] [10] [11] PROCHÁZKA, T. 2009. Altimetry component of a map reconstruction of historical fortification of Špilberk castle. Diploma thesis, Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, 47 pp (in Czech). HONL, I.; PROCHÁZKA, E. 1990. Introduction into History of Surveying. Text book, Czech Technical University, Prague, (in Czech). CHARVÁT, K.; KOCÁB, M.; KONEČNÝ, M.; KUBÍČEK, P. 2007. Geographic Data in Information Society. Research Institute of Geodesy, Topography and Cartography, Zdiby, Czech Republic, year 53, no. 43, 270 pp, (in Czech). BARTONĚK, D.; BUREŠ, J. 2009. Platform for GIS Tuition Usable for Designing of Civil Engineering Structures at Brno University of Technology., Proceedings ICA Symposium on Cartography for Central and Eastern Europe, Research Group Cartography, pp. 955 – 957, Vienna University of Technology, Vienna, Austria, 2009 BARTONĚK, D.; BUREŠ, J.; DRÁB, A.; MENŠÍK, M. 2009. Usage of a Multidisciplinary GIS Platform for the Design of Building Structures., Proceedings Professional Education – FIG International Workshop Vienna, pp. 108 – 118, Austrian Society for Surveying and Geo-information, Vienna, Austria. PUNDT, H. 2002. Field Data Collection with Mobile GIS. Dependencies Between Semantics and Data Quality. In Geoinformatica, vol. 6, no 4, pp 363 – 380. Accessible from http://www.ingentaconnect.com/content/klu/gein/2002/00000006/00000004/05099730 [Pundt et all. 2000] Pundt, H.; Bringkotter, R-Runde, K. 2000: Visualization of spatial data for field based GIS. In Computer & Geosciences. vol. 26, no. 1, pp 51-56. Accessible from WWW:http:/www.iamg.org/CGEditor/cg2000.htm. HITCHCOCK, A.; PUNDT, H.; BIRKKOTTER, R.; RUNDE, K.; STREIT, U. 1996. Data acquision tools for geographic information system. In Geographical Information System International Group (GISIG). (Ed.), Proceedings of the 13th WELL-GIS Workshop on technologies for land management and data supply, RS and GPS Research and Education, June 13, Budapest, Hungary, 3rd session: GIS and Global Positioning System. 8 s. Accessible from http://www.gisis.it/wellgis.www/Budap.htm. VIVONI, E. R.; CAMILLI, R. 2003. Real-time streaming of environmental field data. In Computers & Geosciences., vol. 29, no. 4, pp. 457-468. Accessible from http:///www.iamg.org/CGEditor/cg2003.htm. ADRESS: Ing. Stanislava Dermeková University of Technology, Faculty of Civil Engineering, Institute of Geodesy, Veveří 95 602 00 Brno, Czech Republic [email protected] Assoc. prof. Dalibor Bartoněk EPI Kunovice Osvobození 699, 686 04 Kunovice, Czech Republic, phone: +420-605912767 [email protected] Ing. Irena Opatřilová Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 602 00 Brno, Czech Republic, phone: +420-541147221 [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 26 THE PREDICTION OF SALE TIME SERIES BY ARTIFICIAL NEURAL NETWORK Petr Dostál1, Oldřich Kratochvíl2 1 Brno University of Technology, Faculty of Business and Management, Department of Informatics 2 Private European Polytechnic Institute, Ltd. Kunovice Abstract: The article presents one of the methods of prediction of time series with the support of MATLAB program when Neural Network Toolbox is used. There are mentioned the steps of calculation.The setup of parameters plays a key role for correct prediction. The method of calculation can be used for any time series. Keywords: Prediction, time series, calculation, MATLAB, Neural Network Toolbox 1. INTRODUCTION The article presents the steps of calculation of prediction of sell time series. The Neural Network Toolbox of MATLAB environment is used. The correct prediction is very complicated task because the components of time series in economy and financial are quite often stochastic and random. Therefore the prediction is very difficult and sometimes impossible, when the behaviour of time series is random. This is quite often case of time series on the stock market. A little better situation it is with sale time series. The sale time series include also deterministic components such asperiodicityand/or tendency that are easy recognizable. It could be mentioned consumption or sell of some products, for example week periodicity is caused by behaviour of customers during the week, year tendency is caused by physical phenomena, Gompertz curve is caused by saturation of market, etc. These periodicity and tendency enable reasonable prediction. The case study is focussed on consumption of energy. 2. USED METHODS There are hundreds of methods for prediction of time series. The competitions are held where the best prediction is evaluated. The program MATLAB with Neural Network Toolbox is a strong tool for prediction. The steps of predictions are asfollows: download ofinput and output time series, choice of the type of neural network, set up the number of layers, the number of neurons, transfer functions and some other parameters necessary for the calculation. When the neural network is build up, the process of learning and testing is necessary to run. After the calculation it is necessary to evaluate the results of prediction. The parameters of neural network are possible to change in case of bad prediction. The process of learning and testing is possible repeat several times and with changed parameters. When the prediction is correct,it could be used as a support for decision making for the setup of production plan. The results could be exported for graphical visualisation. 3. CASE STUDY This case study presents the prediction of consumption of energy of a town, where the day and week periodicity is recognisable together with season tendency influence. The behaviour of people and weather could be evaluated as a chaotic. The input data are available at input.csv and output data for learning at target.csv file. The data are downloaded by orders p=(load('input.csv'))'; t=(load('target.csv'))'; nntool and the order nntool for opening neural network is called.The import of input time series is done by means of menu Import p Input data Import OKand output data by means ofmenu Import t Target data Import OK. See Fig.1. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 27 Fig. 1 Import of input and output time series The order New Create displays the screen that enables to choose the type of neural network, the number of layers, the number of neurons, transfer functions and some other parameters necessary for the calculation. The process of build-up of neural network is done by order Create. See Fig.2. Fig. 2 The build-up of neural network The neural network named network1must be trained. The procedure starts by orderTrain-Train Network. The process of training is presented in the window. After the process of training it is possible to use options for display graphs to evaluate the performance. See Fig. 3. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 28 Fig. 3 Displaying the process of training of neural network When the neural network is trained and successfully validated, the data could be exported by the order Export – network1 – Export OK – Close for drawing of real and predicted values of time series. The graph is plotted by orders sim(network1,p); plot(t) hold on plot(ans,'g'). The graph is presented at Fig.4. The graph presents a history of 350 samples and the next 50 samples of prediction. The fig.5 presents zoomed graph of prediction. Prediction Fig. 4 Historical and predicted data of time series ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 29 Fig. 5 Zoomed graph of time series 5. CONCLUSION The sale time series usually contains recognizable tendency and periodicity trends, therefore the predictions gives quite often useful information. The prediction supports right decision when production plan is prepared. LITERATURE [1] DOSTÁL, P. Advance Decision Making in Business and Public Services. Brno : CERM Akademické nakladatelství, 2011. 168 p. ISBN 978-80-7204-747-5. [2] DOSTÁL, P. Pokročilé metody analýz a modelování v podnikatelství a veřejné správě. Brno : CERM, 2008, ISBN 978-80-7204-605-8. [3] THE MATHWORKS. MATLAB – Neural network Toolbox - User’s Guide. The MathWorks, Inc., 2010. ADRESS: Prof. Ing. Petr Dostál, CSc. Brno University of Technology, Faculty of Business and Management, Department of Informatics, Kolejní 4, 612 00 Brno, Tel. +420 541 143714, Fax. +420 541 142 692, [email protected]; h. prof. Ing. Oldřich Kratochvíl, Ph.D., CSc., DrSc., MBA Private European Polytechnic Institute, Ltd. Osvobození 699, 686 04 Kunovice, [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 30 VÝKON DATABÁZOVÝCH SYSTÉMOV NA HARDVÉROVÝCH PLATFORMÁCH Juraj Ďuďák1, Gabriel Gašpar2, Michal Kebísek2 1 Evropský polytechnický institut s.r.o., Kunovice Materiálovotechnologická fakulta so sídlom v Trnave, STU Bratislava, Slovensko 2 Abstrakt: V priemyselných senzorických systémoch sú dôležité viaceré faktory správnej a efektívnej funkcionality. Tieto faktory môžeme rozdeliť na hardvérové a softvérové aspekty. Medzi hardvérové aspekty patrí napríklad výber vhodného zbernicového štandardu na ktorom sú pripojené meracie senzory. Ďalej výber dostatočne výkonnej hardvérovej platformy a zároveň nenáročnej na priestor, inštaláciu a spravovanie a spotrebovanú elektrickú energiu. Medzi softvérové aspekty patrí dostatočne výkonný a spoľahlivý spôsob ukladania dát. V článku bude predstavená myšlienka senzorického systému postaveného na priemyselnom zbernicovom štandarde MODBUS. Ako riadiaci prvok je použité priemyselné riešenie postavené na architektúre ARM - jednodoskové počítače IGEPv2 a PandaBoard. Systém pre ukladanie dát bol zvolený databázový systém MySQL. V článku sú prezentované výsledky záťažových testov databázových systémov na spomínaných harvérových platfomách. Vybrané hardvérové platformy patria medzi aktuálne používané riešenia v priemyselnej sfére. Kľúčové slová: Senzorický systém, merací systém, databázový systém, hardvérové priemyselné platformy ÚVOD Senzorický systém SenSys slúži na zber nameraných údajov. V súčasnosti je podporovaný zber teploty a vlhkosti vzduchu. Výnimočnosť tohto systému je v jeho architektúre. Pri vývoji systému bol kladený veľký dôraz na jednoduchosť implementácie a minimálnu cenu systému. Ďalším aspektom pri vývoji boli funkčné požiadavky. Na systém SenSys sú kladené nároky na rozľahlosť systému (dĺžka zbernice do 2km), mohutnosť systému (počet senzorov do 1000) a rýchlosť odozvy (odozva v rádoch ms). Vďaka použitým technológiám, senzorický systém SenSys tieto požiadavky spĺňa. Základom celého systému je zbernicový štandard MODBUS v úprave uBUS [1] a zbernicový systém 1-Wire. Na Obr. 1 je znázornená principiálna schéma senzorického systému SenSys. Zariadenia DCB sú “Dual Channel Booster”, teda zariadenie, ktoré slúži ako 2-kanálový most medzi zbernicovým systémom uBUS a 1-Wire. Si sú senzory teploty, resp. vlhkosti. Problematike funkcionality blokov DCB a protokolu uBus sa venuje článok [2]. Obrázok 1 Principiálna schéma senzorického systému SynSys Pre správnu funkcionalitu systému SenSys je potrebný počítač, ktorý v celom systéme je v úlohe riadiaceho bloku. Blok PC nemusí byť štandardný osobný počítač, postačí aj priemyselné 1-doskové riešenie ako napríklad IGEP V2 alebo PandaBoard. Pre možnosť neskoršej analýzy nameraných dát, sa tieto dáta ukladajú v bloku PC. Na ukladanie údajov je použitý databázový systém. Ako vhodní kandidáti boli zvolené databázové systémy MySQL a SQLite. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 31 HARDVÉROVÉ RIEŠENIE V tejto kapitole budú predstavené viaceré hardvérové riešenia pre blok PC (z Obr. 1). Ako vhodné riešenia pre použitie v priemysle boli vybrané také architektúry a vyhotovenia, ktoré majú malé fyzické rozmery a nízku spotrebu elektrickej energie. Ako testovacie zostavy poli použité nasledovné riešenia: IGEPv2 PandaBoard Asus EeeBox B202 Procesor Počet jadier Taktovanie RAM Architektúra RS 232 Ethernet WiFi USB Rozširujúce karty Power IGEP v2 ARMv7 Processor rev 2 1 1000 MHz 512 MB ARM Cortex A8 Ano 10/100 eth 802.11b/g 1x MicroSD PandaBoard ARMv7 Processor rev 2 2 1000 MHz 1024 MB ARM Cortex A9 Ano 10/100 eth 802.11b/g 4x SD/MMC Asus EeeBox B202 Intel(R) Atom(TM) CPU N270 2 1600 MHz 1024 MB i686 Nie 10/100 eth 802.11.b/g 4x SD/MMC 5 VDC 5 VDC 19 VDC Tabuľka 1: Hardvérové parametre riadiaceho počítača Na uvedených hardvérových riešeniach bol nainštalovaný databázový server mysql v akruálnych stabilných verziách. Následne bola vytvorená testovacia databáza a naimportované existujúce namerané údaje. Štruktúra testovacej databázy je na obrázku 2. Obrázok 2 Štruktúra testovacej databázy Do tabuliek boli naimportované už namerané dáta: 29722 záznamov v tabuľke sensor_dates a 142709 záznamov v tabuľke sensor_values, čo predstavuje 4 mesiace nepretržitého snímania teplotných hodnôt s intervalom snímania 5 minút s 5-timi teplotnými senzormi. Kernel OS MySQL SQLite IGEP v2 2.6.35.7-16 Ubuntu 10.04 5.1.58-1ubuntu1 sqlite3 3.7.7 PandaBoard 3.0.0-1206-omap4 Ubuntu 11.10 5.1.58-1ubuntu1 sqlite3 3.7.7 Asus EeeBox B202 3.0.0-12-generic-pae Ubuntu 11.10 5.1.58-1ubuntu1 sqlite3 3.7.7 Tabuľka 2 Softvérová konfigurácia použitých riadiacich počítačov ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 32 TESTOVANIE VÝKONNOSTI DATABÁZOVÝCH SERVEROV Pri tvorbe databázových testov sa vychádzalo z budúceho použitia systému. Pri prevádzke systému sa budú namerané hodnoty do databázy zapisovať v dostatočne veľkých intervaloch (niekoľko minút). Bude nás zaujímať rýchlosť operácie vloženia údajov, teda počet operácií INSERT za jednu sekundu a taktiež rýchlosť operácie výberu dát. Pre potreby vyhodnocovania údajov sa budú tieto vyberať z databázy pomocou príkazu SELECT. Pre príkaz výberu SELECT bolo pripravených viacero testov, ktorých úlohou je zistiť výkon databázového servera na danej architektúre pre rôzne typy výberov. Pre testovanie výkonnosti databázových serverov bol vytvorený testovací skript v jazyku Python. Test bol rozdelený na niekoľko častí: test výkonnosti príkazu SELECT: výber hodnôt z jednej tabuľky, použitie agregačných funkcií. V nasledujúcom výpise je skript napísaný v jazyku Python pre meranie času vykonávania pripravených SQL dotazov. def executeQuery(sql): start = time.time() cur.execute(sql) stop=time.time() rows = cur.fetchall() elapsed = (stop - start) return elapsed1,len(rows) Konkrétne SQL dotazy uvádzame priamo v opisoch jednotlivých testov. TESTY S DATABÁZOU MYSQL Na Obr. 2 je logická štruktúra databázových tabuliek nad ktorými budeme robiť testy, ktoré budú zamerané na výkonnosť pri výbere údajov. Test 1: Ako prvý test bude jednoduchý výber údajov nad tabuľkou sensor_values, v ktorej je 140 000 záznamov. Tento test bol realizovaný jednoduchým SQL príkazom: SELECT * FROM sensor_values LIMIT 0,N; kde N bola hodnota od 10000 do 140000 s krokom 10000. Na nasledujúcom grafe (Obr. 3) je znázornená závislosť času vykonania výberu od počtu vyberaných údajov. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 33 Obrázok 3 Výsledok testu 1 Z grafu na Obr. 3 je vidieť, že najrýchlejší výber bol na platforme Atom. Tento výsledok bol zčasti očakávaný, pretože po hardvérovej stránke je táto platforma najvýkonnejšia. Porovnateľnými platformami sú IGEP v2 a PandaBoard. V tomto prípade je rýchlejšie riešenie PandaBoard. V priemere je výber údajov na platforme PandaBoard o 50 % rýchlejší ako na platforma IGEP v2. Treba poznamenať, že PandaBoard je taktovaná skoro s dvojnásobným taktom oproti IGEP v2. Test 2: V druhom teste boli nad celou tabuľkou sensor_values použité agregačné funkcie AVG, MIN, MAX a STD. Zápis v jazyku SQL: SELECT AVG(value),MIN(value), MAX(value), STD(value) FROM sensor_values; Obrázok 4 Výsledok testu 2 Pre testovanie agregačných funkcií bola použitá tabuľka sensor_values. Výsledkom dotazu boli 4 hodnoty vypočítané ako priemerná hodnota (AVG), minumum (MIN), maximum (MAX) a štandardná odchýlka (STD) z hodnôt uložených v stĺpci value. Tieto 4 hodnoty boli vypočítané zo všetkých údajov v tabuľke sensor_values. Na Obr. 4 sú výsledky tohto testu. Opäť je najrýchlejšie na tom platforma Atom, kde bol celkový čas 32ms. Prekvapením tu bol výsledok platformy Igep, na ktorej požadovaný výpočet trval 100ms. Čas pre platformu PandaBoard je o 14% vyšší, teda 114ms. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 34 ZÁVER Cieľom článku bolo zistiť výkonnosť rôznych hardvérových platforiem pre špecifické úlohy. V tomto prípade to bol výkon databázového systému MySQL. Vo všetkých testoch sa pracovalo s rovnakou verziou tohto softvéru. Aby sa dali výsledky vzájomne porovnávať, boli testy vykonávané na rovnakom operačnom systéme. V našom prípade to bol Ubuntu server 11.10, okrem platformy Igep, kde bola k dispozícii len verzia 10.04. Aby sa eliminovali ďalšie vplyvy, daný operačný systém bol nainštalovaný bez grafickej nadstavby a všetky testy boli vykonávané z konzoly. V testoch sa ukázali najväčšie rozdiely medzi hardvérovou architektúrou medzi ARM a x86 v prospech architektúry x86. Rozdiely vo výkone pri architektúre ARM mohli byť spôsobené samotným počtom jadier CPU (1 pri IGEP v2 a 2 pri PandaBoard), avšak zistené výsledky sú porovnateľné. REFERENCIE [1] DUDAK, J. The Contribution to Industrial Communication Standards. In: INFORMATION SCIENCES AND TECHNOLOGIES BULLETIN OF THE ACM SLOVAKIA. - ISSN 1338-1237. - Vol. 2, No. 1 (2010), p. 34-41. [2] DUDAK, J.; GASPAR, G.; KEBISEK, M. APPLICATION OF MODIFIED MODBUS PROTOCOL FOR THE NEEDS OF MODERN MEASUREMENT SYSTEMS, In: Proceedings of the International Conference on Advances in Mechatronics 2011 (AIM’11), University of Defence, Faculty of Military Technology, Brno, 2011, ISBN 978-80-7231-848-3, pp. 9-14 [3] ISEE : IGEPv2 Board, online: http://www.igep.es/index.php?option=com_content &view =article&id=46&Itemid=55. [4] pandaboard: online:<http://pandaboard.org/> [5] MAGA, D.; WAGNER, J. Ultra High Torque SRM - Measurement and Computer Design. Compel – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering. 1998, Volume 17, Number 1/2/3, s. 364 – 368. ISSN 0332-1649. [6] SLOVÁČEK, D.; JANOVIČ, F. Efficiency Network Regulated By Linux. In ICSC 2010. Kunovice : EPI, s.r.o, 2010. ISBN 978-80-7314-201-8. ADRESA: Ing. Juraj Ďuďák, PhD. Evropský polytechnický institut , s.r.o. Osvobození 699 686 04 Kunovice, Česká republika [email protected] Gabrie Gašpar Materiálovotechnologická fakulta so sídlom v Trnave STU Bratislava, Slovensko Michal Kebísek Materiálovotechnologická fakulta so sídlom v Trnave STU Bratislava, Slovensko [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 35 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 36 DATA ANALYSIS & MODELING USING OPEN SOURCE SOFTWARE R Lukáš Falát University of Žilina, Faculty of Management Science & Informatics, the Slovak Republic Abstract: This paper deals with data analysis and modelling of Open Source Software R. Firstly, R software is generally presented as a free alternative to commercial programs such as SPSS or SAS. Later main features of R Project and main advantages of this program are also discussed. Finally, a financial application of exchange rate is performed in order to illustrate work with this software as well as the wide range of R usability. Keywords: R, Open Source, packages, data analysis, financial analysis, data mining, data modelling, ARIMA, GARCH, ARCH, time series 1 INTRODUCTION Nowadays, to be able to analyse huge amount of data, find there interesting information and then construct a model is very important and demanding from many scientists, engineers and statisticians from all over the world, no matter what a real problem is. It can include how to distinct spam from normal message, how to find out the development of human population or set the tomorrow’s price of corn on world markets. These examples have something in common. In all cases one has to create a right model before knowing answer to these questions. As the problems of real world are quite complex, data analysis as well as constructing models is sometimes not as simple and it often demands lot of time and number of tests to find out something important or to declare the model is correct. And as we are living in the information era, computers come in handy in this case. However, today there exists a huge number of special programs for data modelling. They can differ in what area of modelling they are used in but very often, what they differ in is mainly price for the software. It is true that commercial programs such as SPSS, SAS or Eviews dispose by a large number of functions, they are very user friendly, they have beautiful graphs and outputs, the documentation is also on high level. But the main disadvantage of these programs is their price. They cost very much money and even if it is not a big deal for an IT company, there is only small amount of schools, universities and other non-profit institutions that can afford to buy this kind of software. 2 R PROJECT Fortunately, for those kind of people, open source programs exist. One open source software for data mining, modelling and analysis is called R. Project R is very popular among lots of universities all over the world. Moreover, as data mining has entered a golden age, R has become a major tool for plenty of statisticians, engineers or mathematicians, whether being used to set ad prices, find new drugs more quickly or fine-tune financial models. Companies as diverse as Google, Pfizer, Merck, Bank of America, the InterContinental Hotels Group and Shell use it, too. R first appeared in 1996, when the statistics professors Ross Ihaka and Robert Gentleman of the University of Auckland in New Zealand released the code as a free software package. They both wanted technology better suited for their statistics students, who needed to analyze data and produce graphical models of the information. The software itself can be downloaded on the webpage http://www.r-project.org. This tool is also great for statisticians and mathematicians as it contains lots of build in statistical functions. The main advantages of this software include: Easy accessibility. The program is for free as it belongs to the Open Source software. Active user support all over the world. It runs on various platforms including Windows, Linux and MacOS. Wide range of constructed functions. There exists hundreds of packages (more than 1600), each of them specializing in some specific area (machines, genome analysis, financial analysis,…). A large, coherent, integrated collection of intermediate tools for data analysis. Great plots and graphical facilities for data analysis. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 37 As stated above, a thing what makes R so useful — and helps explain its quick acceptance — is that statisticians, engineers and scientists can improve the software’s code or write variations for specific tasks. Packages written for R add advanced algorithms, colored and textured graphs and mining techniques to dig deeper into databases. For example, a package, called BiodiversityR, offers a graphical interface aimed at making calculations of environmental trends easier. Another package, called Emu, analyzes speech patterns, while GenABEL is used to study the human genome. The financial services community has also demonstrated a particular affinity for R; dozens of packages exist for financial analysis alone. 3 APPLICATION The strengths of R project will be illustrated on financial modelling of time series of AUD/USD exchange rate, to see wide range of specialized applications where this software can be applied. The packages which have been used for this illustrative application include: FinTS, fGARCH, tseries, zoo, stats. The data include exchange rate data of AUD/USD from November 2005 to November 2010. The aim was to analyse the data, then model this exchange rate and finally verify if our model was constructed correctly. The first step was to load appropriate libraries and load our data: library(xlsReadWrite) library(stats) my_data = read.xls("D:\\AU.xls", colNames=TRUE, type="double", sheet=1, from=1) 3.1 DATA ANALYSIS AND MODEL CONSTRUCTION Next step in modelling a specific problem is to have correct data. Very often real data are biased; it means that they are influenced by some external factors and therefore cannot be used alone without being dependent on something else. In other word we want the data or the time series be independent or stationary. Otherwise, the results of analysis and the constructed models would not be considered to be right and correct. There exists various options how to determine the stationarity of time series, probably the most popular are stationarity tests such as ADF test or Ziwhat-Andrew. It is no surprise that R financial packages support also this feature. KPSS test which is the same type of test and which can be found in tseries package is great for findind this out: Kpss.test(my_data) The KPSS test confirmed that the series was not stationary and therefore must be transformed into stationary series. This was done by data differentiating. Analysing of this data was performed using knowledge from specific area (financial econometrics). Knowing from econometrics area, the tools for autocorrelation function (ACF) and partial autocorrelation function (PACF) and Akaike Information Criteria (AIC) are excellent aid in this case. No surprise R has all this stuff. In R, ACF is defined as acf( x, lag.max = NULL, type = c("correlation", "covariance", "partial"), plot = TRUE, na.action = na.fail, demean = TRUE, ...) For our purposes, it is enough to use only our data series variable. As seen from the command, the ACF can be also presented into graph. PACF function is defined in a similar way. However, by analysing the differentiated versions of our data, we were not able to determine any trend in the series. AIC criteria which is a penalty function may come in handy in this case. In R, for specific model, it is defined as a negative number and can be found in the model summary. The more negative the number is, the better the model is. For example, for a model arima (2,2,2), which is a typical econometric model, the AIC is in the figure 1 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 38 Figure 5 The Summary of ARIMA (2,2,2) By analysing AIC of several models, we found out that ARIMA (1,2,1) was the best model. Table 1 AIC values of tested models We determined the model for AUD/USD exchange rate in R as ARIMA (1,2,1). The next step was to verify this model. 3.2 MODEL VERIFICATION The verification of the model include verification of residuals of the model. This can be done by ARCH test: ArchTest(residuals$arima11, lags = 1) ArchTest(residuals$arima11, lags = 5) ArchTest(residuals$arima11, lags = 12) On base of small value of p-value it was clear that residuals were not independent and there existed some ARCH effect. This could be removed by incorporating ARCH into our model. In our case, this model definition looked like this: model = garchFit(~arma(1,2,1)+garch(1, 1), data =my_data) summary(model) We hence edited the model by adding the GARCH(1,1) part into the default model. As previously, residuals of this model must have been checked too. GarchRezidua = model@residuals/[email protected] ArchTest(GarchRezidua, lags = 1) ArchTest(GarchRezidua, lags = 5) ArchTest(GarchRezidua, lags = 12) On base of p-value larger than significance level, one could say the residuals were now independent and the model was correct. The correctness of this model could be also checked graphically. x11() plot(density(Garch Residuals),main="Distribution of Garch reziduals") curve(dnorm(x,m=-0.001742,sd=0.9966694),from=-5,to=5, main="Normal distribution", col="red", add=TRUE) ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 39 Figure 6 Density Distribution of Residuals of Model Graphical control was also all right and therefore we could say that final financial model for AUD/USD exchange rate was ARIMA (1,2,1) + GARCH (1,1). Finally, figure 3 shows the historical values of time series (green colour) and model-estimated values (red colour) for graphical control. Figure 7 Historical values (green) of time series and estimated values (red) of the model 4 CONCLUSION In this paper the Open Source Software for data analysis and modelling was presented. The main advantages of this program were discussed, among other it is mainly a huge number of packages with very wide range of special usability. This feature has been illustrated with a financial modelling example. The AUD/USD exchange rate was analysed, then the model was created and verified. Commands in R have been presented, too. As seen above, the commands must be typed into the console and there is no clicking interface. However, R commands are usually very user-friendly oriented and simple. Moreover, usually there are lots of manuals of packages and even plenty of examples which can be used in your R analysis and modelling. REFERENCES [1] FALÁT, L. Econometric Modelling on Forex Market: Application of ARIMA and GARCH Models to Specific Exchange Rates Data, International Masaryk Conference for Doctoral Students and Young Scientists, Hradec Králové, the Czech Republic, 2011. [2] FALÁT, L.; LAŠTÍK, T.; TKÁČ P. FRI R Manual, 2011, 44p [online] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 40 [3] [4] [5] [6] [7] [8] MARČEK, M. Viacnásobná štatistická analýza dát a modely časových radov v ekonómii, Opava : Silesian University, 2009. 242 p. MARČEK, D.; MARČEK, M.; PANČÍKOVÁ, L. Econometrics and Soft Computing, Žilina : EDIS, University of Žilina, 2008. 272 p. MONTGOMERY, D. C.; JENNINGS, C. L.; KULAHCI, M. Introduction to Time Series Analysis and Forecasting, New Jersey : John Wiley & Sons, Inc, 2008. VANCE, A. Data Analysts Captivated by R’Power, [online], 07/01/2009, NYTimes.com The R Project Homepage [online], 11/14/2011, www.r-project.org ZIVOT, E.;, WANG, J. Modelling Financial Time Series with S Plus, Springer, 2003, 632 p. ADDRESS Ing. Lukáš Falát University of Žilina Faculty of Management Science & Informatics the Slovak Republic ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 41 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 42 OPTIMISATION OF DECOMPOSITION STRATEGIES IN PARALLEL ALGORITHMS Ivan Hanuliak European polytechnic institute, Kunovice Abstract: The article is devoted to the important role of decomposition strategy in parallel computing. This influence is illustrated on the example of very frequently used parallel algorithm and that is matrix multiplication. On the basis of the done analysis of the used parallel computers in the world these are divided to the two basic groups which are from the programmer-developer point of view very different. They are also introduced the typical principal structures for both these groups of parallel computers and also their models. The paper then in an illustrative way describes development of concrete parallel algorithm for matrix multiplication on various parallel systems. For each individual practical implementation of matrix multiplication there is introduced the derivation of its calculation complexity. The described individual ways of developing parallel matrix multiplication and their implementations are compared, analysed and discussed from sight of programmer-developer and user in order to show the very important role of decomposition strategies mainly at the class of asynchronous parallel computers. Keywords: parallel computer, synchronous and asynchronous parallel system, systolic system, matrix multiplication, decomposition method 1. INTRODUCTION It is very difficult to classify the existed parallel system. From the point of programmer-developer I divide, after the done analysis [2, 3], parallel computers to the following two different groups synchronous parallel architectures. They are typical through the handling mutually independent or noninteracted processes. These are used for performing the same computation on different sets of data. They can be used under central control, that means under the global clock synchronisation (vector, array system etc.) or a distributed local control mechanism (systolic computer etc.). The dominant system property is the concentration to data parallelism. The typical example of synchronous parallel computer illustrates Fig. 1. asynchronous parallel computers. They are composed of a number of independent processors or computers. From the point of programmer it is typical for their application using (co-operation and synchronisation of processes) mutual inter process communications (IPC). To this group belong mainly computer networks based on network of workstation (NOW|) according Fig. 2. Host computer Shared memory Control computer … … … Array of processors (compute nodes) … Fig. 1. Typical synchronous parallel system. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 43 There has been an increasing interest in the use of networks (Cluster) of workstations connected together by high speed networks for solving large computation intensive problems. This trend is mainly driven by the cost effectiveness of such systems as compared to massive multiprocessor systems with tightly coupled processors and memories (Supercomputers). Parallel computing on a cluster of workstations connected by high speed networks has given rise to a range of hardware and network related issues on any given platform. Load balancing, inter processor communication (IPC), and transport protocol for such machines are being widely studied [9, 11,]. With the availability of cheap personal computers, workstations and networking devises, the recent trend is to connect a number of such workstations to solve computation intensive tasks in parallel on such clusters. Network of workstations (NOW) [13, 16, 18] has become a widely accepted form of high performance computing (HPC). Each workstation in a NOW is treated similarly to a processing element in a multiprocessor system. However, workstations are far more powerful and flexible than processing elements in conventional multiprocessors (Supercomputers). To exploit the parallel processing capability of a NOW, an application algorithm must be paralleled. A way how to do it for an application problem builds its decomposition strategy. This step belongs to a most important step in developing parallel algorithm [8, 10, 14] and their performance modelling and optimization (Effective parallel algorithm). Local memory Processor Processor Local memory Processor Local memory Communication network Local memory Processor Fig. 2. Typical asynchronous parallel system. 2. PARALLEL ALGORITHMS The role of programmer is for the given parallel computer and for the given application task (Complex application problem) to develop the effective parallel algorithm. This task is more complicated in those cases, in which he must create the conditions for the parallel activity, that is through dividing the input algorithm to many mutual independent parts (Decomposition strategy), which are named processes or threads. In general development of the parallel algorithms include the following activities [4, 5, 6] decomposition - the division of the application into a set of parallel processes and data mapping - the way how processes and data are distributed among the nodes of a parallel system inter process communication (IPC) - the way of cooperation and synchronization tuning – performance optimisation of a developed parallel algorithm. The most important step is to choose the best decomposition method for given application problem [3, 12]. To do this it is necessary to understand the concrete application problem, the data domain, the used algorithm and the flow of control in given application. When designing a parallel program the description of the high level algorithm must include, in addition to design a sequential program, the method you intend to use to break the application into processes or threads (Decomposition strategy) and distribute data to different nodes (Mapping). ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 44 The chosen decomposition method drives the rest of program development. Quantitative evaluation and modelling of hardware and software components of parallel systems are critical for the delivery of high performance. Performance studies apply to initial design phases as well as to procurement, tuning, and capacity planning analysis. As performance cannot be expressed by quantities independent of the system workload, the quantitative characterization of resource demands of application and of their behaviour is an important part of any performance evaluation study. Among the goals of parallel systems performance analysis are to assess the performance of a system or a system component or an application, to investigate the match between requirements and system architecture characteristics, to identify the features that have a significant impact on the application execution time, to predict the performance of a particular application on a given parallel system, to evaluate different structures of parallel applications. To the performance evaluation we briefly review the techniques most commonly adopted for the evaluation of parallel systems and its metrics. 3. THE ROLE OF PERFORMANCE Quantitative evaluation and modelling of hardware and software components of parallel systems are critical for the delivery of high performance. Performance studies apply to initial design phases as well as to procurement, tuning and capacity planning analysis. As performance cannot be expressed by quantities independent of the system workload, the quantitative characterisation of resource demands of application and of their behaviour is an important part of any performance evaluation study [1, 15]. Among the goals of parallel systems performance analysis are to assess the performance of a system or a system component or an application, to investigate the match between requirements and system architecture characteristics, to identify the features that have a significant impact on the application execution time, to predict the performance of a particular application on a given parallel system, to evaluate different structures of parallel applications. In order to extend the applicability of analytical techniques to the parallel processing domain, various enhancements have been introduced to model phenomena such as simultaneous resource possession, fork and join mechanism, blocking and synchronisation. Modelling techniques allow to model contention both at hardware and software levels by combining approximate solutions and analytical methods. However, the complexity of parallel systems and algorithms limit the applicability of these techniques. Therefore, in spite of its computation and time requirements, simulation is extensively used as it imposes no constraints on modelling. Evaluating system performance via experimental measurements is a very useful alternative for parallel systems and algorithms. Measurements can be gathered on existing systems by means of benchmark applications that aim at stressing specific aspects of the parallel systems and algorithms. Even though benchmarks can be used in all types of performance studies, their main field of application is competitive procurement and performance assessment of existing systems and algorithms. Parallel benchmarks extend the traditional sequential ones by providing a wider a wider set of suites that exercise each system component targeted workload. 4. SYNCHRONOUS MATRIX MULTIPLICATION 4.1. A SYSTOLIC MATRIX MULTIPLIER We now consider an example of the systolic multiplication of two matrices A (km) and B (mn). The algorithm for matrix multiplication that is most suited is based on outer products rather than the conventional inner product method. Here we evaluate k N A.B C ( p).R( p) p 1 where C( p) R( p) c pj rpj p 1,2,...,k , and j=1,2,...,n. Here C(p) is a k~n matrix with all the columns identical with the p-th column of A and R(p) is a k~n matrix with all the rows identical with the p-th row of B. For example if: a11 a12 a13 A a 21 a 22 a 23 b11 b12 B b21 b22 b31 b32 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 45 then N=A.B=C(1).R(1)+C(2).R(2)+ C(3).R(3) N a11b11 a 21b11 a11b12 a12 b21 a 21b12 a 22 b21 a12 b22 a13 b31 a 22 b22 a 23 b31 a13b32 a 23b32 A systolic matrix multiplier is shown in Figure 3. The input streams of the rows of A arrive from the left , and the input streams of columns of B arrive from the top of nodes N 11,N12,N21 and N22. Each of these nodes has the capability of multiplying two inputs numbers and holding the result until the next set of inputs arrives for multiplication; then the sum is accumulated and the process is repeated. Note that the product matrix N is finally available at the nodes N 11,N12,N21 and N22. Thus in this case the matrix is entirely mapped in one-to-one correspondence to the processor array. The time taken to multiply two matrices of size k m and m n with using k x n processors is m+(k-1)+(n-1) time units. This result is easily proved using the fact that the last computation are carried out after a lapse of (k1)+(n-1) units, because of the skewing of the matrices, and it takes m units of time to multiply two vectors of size m. Note that a conventional single-processor matrix multiplication requires k.m.n operational time units; in the case of the systolic multiplier we use k x n processors (or more space) to reduce the time to m+n+k-2. Fig. 3. Systolic matrix multiplier. 5. THE ASYNCHRONOUS MATRIX MULTIPLICATION Principally development of the asynchronous parallel algorithm include the following activities [7, 17] 3) Decomposition - the division of the application into a set of parallel processes and data. This is the most important step at developing asynchronous parallel algorithm. 4) Mapping - the way how processes and data are distributed among the nodes of used parallel systems (processors or working stations) 5) Interprocess communication - the way of corresponding and synchronisation among individual processes 6) Tuning - alternation of the working application to improve performance (performance optimisation) 5.1. DECOMPOSITION STRATEGIES To choose the best decomposition method for any application, we have to understand the concrete application problem, the data domain, the used algorithm and the flow of control in given application. Therefore we can use according the concrete character of given task the following decomposition models [3, 12] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 46 perfectly parallel decomposition domain decomposition (suitable for matrix multiplication) control decomposition: functional manager/workers object-oriented programming OOP ( modern object oriented programming technology) 5.2. DOMAIN DECOMPOSITION METHODS FOR MATRIX MULTIPLICATION We will illustrate the role of right decomposition strategies just on matrix multiplication. The principle of matrix multiplication we illustrate for simplicity for the matrixes A, B with numbers of rows and columns k=2. The result matrix C=A x B is: a11 a 21 a12 b11 b12 a11 b11 a12 b21 a22 b21 b22 a21 b11 a22 b21 a11 b12 a12 b22 c11 a21 b12 a22 b22 c21 c12 c22 The way of sequential calculation is following Step 1: Calculate all the values of the result matrix C for the first row of matrix A and for all columns of the matrix B Step 2: Take the next row of matrix A and repeat step 1. In this procedure we can see the potential possibility of parallel calculation, that is the repetition of activities in the step 1 always with the another row of matrix A. Let consider the calculation example of matrix multiplication on parallel system. The basic idea of the possible decomposition procedure illustrates Fig.4. A´i B´i = C´i i Fig. 4. Decomposition of matrix multiplication through the rows of the first matrix. The procedure is as following: Step 1: Give to the i-th node horizontal column of the matrix A with the names A´i and i-th vertical column of the matrix B named as B´i Step 2: Calculate all values of the result matrix C for A´i and B´i and named them as C´ii Step 3: I-th node give its value B´i to the node i-1 and get B´i+1 value from i+1-th node. Repeat the steps 2 and 3 to the time till i-th node does not calculate C´i,i-1 values with B´i-1 columns and row A´i. Then i-th node calculated i-th row of the matrix C (Fig. 5.) for the matrix B with the number k-columns. The advantage of such chosen decomposition is the minimal consume of memory cells. Every node has only three values (rows and columns) from every matrix. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 47 C´i , 1 ... C´i , i - 2 C´i , i - 1 C´i , i C´i , i + 1 C´i , i + 2 ... C´i , k . Fig. 5. Illustration of the gradually calculation of matrix C. This method is also essential fast as the second possible way of decomposition according Fig. 6. A´i B´i C´ Fig. 6. Decomposition of matrix multiplication with using the rows of first matrix. The procedure is following: Step 1: Give to the i-th node vertical column of the matrix A (A´i) and the horizontal row of the matrix B (B´i). Step 2: Perform the ordinary matrix calculation A´i and B´i. The result is the matrix C´i of type n x n. Every element from C´i is the particular element of the total sum which corresponds to the result matrix C. Step 3: Call the function of parallel addition GSSUM for the creating of the result matrix C from the corresponds elements C´i. This added function causes increasing of the calculation time, which strong depends on the magnitude of the input matrixes (Fig. 7.). n C´3(1,1) C´3(1,2) C´2(1,1) C´2(1,2) C´3(2,1) C´1(1,1) C´1(1,2) C´1(2,1) ad dit io C(1,1) C(1,2) C(2,1) = C´1(2,1) Fig. 7. Illustration of the gradually calculation of the elements C´i,j. Let k be the magnitude of the rows or columns A, B and U defines the total number of nodes. Then: C1 1,1 a1,1 b1,1 a1, 2 b1, 2 . . . a1,k b1,k C2 1,1 a1,k 1 b1,k 1 a1,k 2 b1,k 2 . . . a1, 2k b1, 2k . . . . CU 1,1 a1,(U 1) k 1 b1,(U 1) k 1 . . . a1, Mk b1, Mk and the finally element of matrix C ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 48 U C 1,1 Ci 1,1 i 1 50,0 D e c o m p o s i t i o n1 D e c o m p o s i t i o n2 Time [s] 40,0 30,0 20,0 10,0 0,0 5,0 10,0 15,0 Number of compute nodes Figure 8. Optimisation of decomposition methods at matrix multiplication. 6. THE RESULTS The comparison on both decomposition strategies for various number of compute node illustrates Fig. 9. The first chosen decomposition method go straightforward to the calculation of the individual elements of the result matrix C through multiplication of the corresponds matrix elements A and B. The second decomposition method for the getting the final elements of the matrix C besides multiplication of the corresponded matrix elements A and B demand the additional addition of the particular results, which causes the additional time complexity in comparison to the first used method. This additional time complexity depends strong on the magnitude of the input matrixes as you can see from the Figure 8. 7. CONCLUSIONS AND PERSPECTIVES On the given simple example of matrix multiplication I demonstrated the great influence of optimisation of decomposition strategies to the whole complexity of parallel algorithms. The using of parallel systems to this time showed unambiguous that the parallel architectures of the computer systems belong to the most effective and rational ways of increasing the computer system performance also in the future time. The various in the world successful widespread synchronous parallel architectures have not been expanded in our country from the various causes and in relation to the latest trends in the world they will not be expanded in the future. In spite of it the dynamic growth in our country we can see just in the asynchronous parallel architectures and specially symmetrical multiprocessors and local area networks of personal computers. The last one are independent from the still very low technical level of the remote telecommunication lines in our country. Therefore we are also using to the practical implementations of parallel algorithms the build integrated heterogeneous computer network of personal computers at my working place. One node of our computer network is also the powerful multiprocessor parallel system (symmetrical multiprocessor). REFERENCES [1] GELENBE, E. Computer system performance modeling in perspective, 288 pages, published September 2006, Imperial College Press. [2] HANULIAK, I. Paralelné počítače a algoritmy, 327 pp., Vyd.: ELFA Košice, 1999. [3] HANULIAK, I. Paralelné architektúry – multiprocesory, počítačové siete, Žilina : Vyd.: Knižné ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 49 [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] centrum, 1997, 187 pp. HANULIAK, P. Virtual parallel computer, In Proc.: TRANSCOM 2007 - section 3, Žilina : 2007. pp. 71-74 HANULIAK, P.; VARŠA, P. To performance evaluation of Jacobi iteration, In Proc.: TRANSCOM 2003, Žilina : 2003. pp. 69-72 HANULIAK, P. Parallel iteration algorithms for Laplacean equation method, ICSC 2012, section 2, pp 1 - 8, Kunovice, Czech republic (in print). HANULIAK, P.; SLOVÁČEK, D. To performance modeling of virtual computers, In Proc.: TRANSCOM 2011 - section 3, Žilina : 2011. pp. 213 – 216 HUDIK, M. Performance optimization of broadcast collective operation on multi-core cluster, ICSC Leden 2012, Kunovice : Czech republic (in print). HUDIK, M.; HANULIAK, P. Analysing Performance of Parallel Algorithms for Linear System Equations, In Proc.: GCCP 2011, October 24-26, SAV Institute of Informatics, Bratislava : 2011. pp. 70-77 HUDIK, M.; HANULIAK, P. Parallel complexity of linear system equation, In Proc.: TRANSCOM 2011 - section 3, Žilina : 2011. pp. 107-110 JANOVIČ, F.; HOLÚBEK, A. Load balance and data decomposition for distributed prime number algorithm, In Proc.: TRANSCOM 2011, Žilina : 2011. pp. 99 - 101 JANOVIČ, F. Modelovanie výkonnosti distribuovaných paralelných algoritmov, ICSC Leden 2012, Kunovice : Czech republic (in print). KIRK, D. B.; HWU, W. W. Programming massively parallel processors, Morgam Kaufmann, 280 pages, 2010. KUMAR, A.; MANJUNATH, D.; KURI, J. Communication Networking, Morgan Kaufmann, 2004. 750 pp. LILJA, D. J. Measuring Computer Performance, University of Minnesota, Cambridge University Press, United Kingdom : 2005. 280 p. PATERSON, D. A.; HENNESSY, J. L. Computer Organisation and Design, Morgan Kaufmann : 2009. 912 pp. SLOVÁČEK, D.; HANULIAK, P. Analysis of computer performance, In Proc. MMK 2010, 6.-10 Prosinec, Hradec Králové : Czech republic, 2010. pp. 42-51 SLOVÁČEK, D. Modelovanie výkonnosti viacprocesorových paralelných systémov, ICSC Leden 2012, Kunovice : Czech republic (in print). ADDRESSEE Prof. Ing. Ivan Hanuliak, CSc. European Polytechnic Institute Osvobozeni 699 686 04, Kunovice [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 50 PERFORMANCE OPTIMIZATION OF BROADCAST COLLECTIVE OPERATION ON MULTI-CORE CLUSTER Hudik Martin University of Zilina, Faculty of Control and Informatics, Zilina, Slovana Abstract: Current trends in high performance computing (HPC) and grid computing (Grid) are to use networks of workstations (NOW) as a cheaper alternative to traditionally used massively parallel multiprocessors or supercomputers. Today computers consist of processor which has more than one core. Is not unusual to have computer with a processor with four and more cores in combination with SMP. For effective use of such a parallel machines it is crucial to know it limitations (bottlenecks). This paper analyses "broadcast" a basic cooperative communication operation in light of using multi-core cluster. The focus is put in its bottlenecks as they are in many parallel systems the limiting factor of the maximum rate of parallelization. In this paper, analysis focus on performance difference when normal MPICH2 broadcast is used with different processes scheduling strategies. In the end customized broadcast is revealed as best solution for multi-core environment. This customized broadcast distinguishes between intra-node and inter-node communication and so it divide one communication domain into sub-domains. Keywords: parallel computer, parallel algorithm, performance modeling, multi-core, broadcast, collective operation 1 INTRODUCTION Nowadays if we look on small cheap cluster solutions or big clusters rated by Top500.org we can say that for these platforms multi-core processor architecture is dominant. Performance of multi-core computers dramatically increases compare to single processor computer [1, 12]. Combination with fast interconnection network with high bandwidth and low latency will create cluster with massive computational power. Multi-core cluster can speed up application performance and scalability [11, 13]. This massive computational power needs deep understanding of multi-core characteristic and their influence in application behavior. To exploit the parallel processing capability of a cluster, an application algorithm must be paralleled. The role of programmer is to develop the effective parallel algorithm [3, 5] for the given parallel computer and for the given application task. In general development of the parallel algorithms include the following activities decomposition - the division of the application into a set of parallel processes and data [2, 4, 6] mapping - the way how processes and data are distributed among the computational nodes [7] inter process communication (IPC) - the way of cooperation and synchronization [10] tuning – performance optimization of a developed parallel algorithm.[3, 8] The most important step is to choose the best decomposition method for a given application problem [9]. MPI become a primary programming paradigm for writing parallel algorithms. It provides building blogs for developing parallel algorithms such as methods for point-to-point communication and cooperative communication. There are many implementations of MPI standard one of them is MPICH [15]. This implantation takes into account shared-memory architecture in sense of choosing appropriate communication method. 1.1 BACKGROUND In this paper we assuming that every node in cluster is a multi-core computer with only one network adapter (NIC). Computers in the cluster are connected together with high-performance switch so that all nodes in a single cluster can communicate with each other without performance degradation [12]. We use MPICH2 as the MPI implantation. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 51 1.2 MPICH2 The communication portion of MPICH2 is implemented in several layers, as shown in Figure 1, and provides two ways to port MPICH2 to a communication subsystem. The ADI3 layer presents the MPI interface to the application layer above it, and the ADI3 interface to the device layer below it. MPICH2 can be ported to a new communication subsystem by implementing a device. The CH3 device presents the CH3 interface to the layer below it, and provides another way for MPICH2 to be ported to a new communication subsystem: by implementing a channel. Fig. 1. Layers of MPICH2 1.3 CH3: NEMESIS The Nemesis communication subsystem was designed to be a scalable, high-performance, shared-memory, multinetwork communication subsystem for MPICH2. This communication channel offers universal solution for intranode and internode communication. Its universality lays in automatic choosing appropriate method for sending a message. To achieve the high scalability and low intranode overhead, Nemesis communication channel was designed using lock-free queues in shared memory. Thus, each process needs only one receive queue, onto which other processes on the same node can enqueue messages without the overhead of acquiring a lock. 2 MPI BROADCAST MPICH2 uses different collective algorithms for small and large messages [15]. For sending small messages MPICH uses binominal tree algorithm (Fig 2.) and for large messages van de Geijn Algorithm (Fig 3.). 3 6 7 2 4 5 3 2 3 1 3 2 0 1 3 Fig. 2. Binominal tree algorithm on hypercube Fig. 3. Van de Geijn algorithm ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 52 Binomial Tree. Figure 2 shows hypercube structure. In the first step, the root sends the whole message to node which is half of the maximum distance (p=4). Next, the root and p=4 send the message to next half node p=6 and (0=2)p, respectively. Then the algorithm is continued recursively. While this algorithm is preferred for small messages, it is not suitable for large messages. This is because some nodes send the whole message several times. van de Geijn Algorithm As described in Figure 3, this algorithm consists of two phases. The first phase is scatter when the message is divided and scattered among all nodes by using a binomial tree. The second phase is allGather when divided messages are collected by using recursive doubling technique. Then the whole message becomes available in every node. Algorithm Time complexity Binominal tree van de Geijn Table 1. Summary of communication times for discussed broadcast algorithms. The message size is m and the number of nodes is p. ts constant is start time for sending message and tw is constant representing sending one word of message. 3 CASE STUDY: MPI BROADCAST ON CLUSTERS WITH MULTI-CORE-PROCESSOR NODES For clusters that consist only from single-core-processor nodes table 1 shows the summary of estimated cost of broadcast algorithms. Assuming that the cluster is centralized this estimated cost are not dependent on process scheduling or location of root process. On the other hand on cluster that consist from multi-core or SMP nodes the estimated cost are dependent on process scheduling and location of root process. This is valid under the assumption that each node has only one network adapter. Fig. 4. Case study of broadcast operation on multi-core nodes cluster with use of round robin process scheduling We present a case study of binominal tree algorithms on multi-core cluster. Figure 4 shows a steps of this algorithm. Every node consist of computer with dual core processor. The processes are scheduled with round robin algorithm. As we can see with this algorithm (described in section 3) some steps are done dually from one node, trough one network adapter. The estimate cost almost doubles compare to single-core configuration of cluster. To avoid this slow down the block scheduling method can be used. Measurements for this case study was done on cluster which consists of 8 computers and each of them has quad core processor. They were connected together according Fig.4. From the Figure 5 we can see the difference between two scheduling methods. The preliminary conclusion can be made, that for the clusters with multi-core, SMP computers the block scheduling method is more efficient than the round robin. It’s because the messages within one computer are send through shared memory using Nemesis module. The block method make explicitly use of multi-core, SMP environment. Sending-receiving time of broadcast stays approximately constant. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 53 Processes Scheduling method 8 ---- Data out [MB] --- Data in [MB] --- Packet out Packet in --- --- Time [s] 31,6 16 Round Robin 4591 3260 285912 544760 53,6 16 Block 3071 1650 155194 344917 31,7 32 Round Robin 8146 6810 561392 921838 93,4 32 Block 3251 1706 153896 345428 35,2 Table 2. Measurement result from case study Fig. 5. Broadcast time comparison between round robin and block scheduling 4 CONCLUSION Today, most supercomputers and clusters are based on multi-core processors or SMP, but not all applications benefit from them[14]. The current version of MPICH2 isn't fully adopted for multi-core, SMP supercomputer environment. There were made some improvements, on communication layer focusing on point to point communication, when nemesis communication subsystem module was presented. Collective operation stays unaware of multi-core, SMP environment. Lot of exiting parallel applications can benefit from improved collective operations that are aware of multi-core environment. In this paper we present a analysis of broadcast collective operation in multi-core environment. We compared two different scheduling methods for assigning processes to processors, round robin and block scheduling method. From our research and measurements we can say that the more efficient is the block scheduling method. Some existing applications can benefit from using block scheduling method, specially applications in which the root sending process doesn't change during the computation. If we want more universal solution for all sorts of application, customized broadcast need to be presented. Figure 6 shows customized broadcast operation in which one broadcast domain is divided according physical computer parameter to small broadcast domains. This customized broadcast isn't dependent on any scheduling method or root sender location. Fig. 6. Customized Broadcast with divide communication domains ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 54 REFERENCES [1] GELENBE, E. Computer system performance modeling in perspective, 288 pages, published September 2006, Imperial College Press [2] HANULIAK, I.; HANULIAK, P. Performance evaluation of iterative parallel algorithms, Kybernetes, Volume 39, No.1, United Kingdom : 2010, pp. 107- 126 [3] HANULIAK, I.; HANULIAK, P. To performance modelling of parallel algorithms, ICSC 2011, sekcia č. 2, pp 125 - 132, Kunovice, Czech republic [4] HANULIAK, P. Parallel iteration algorithms for Laplacean equation method, ICSC 2012, section 2, pp 1 - 8, Kunovice, Czech republic (in print) [5] HANULIAK, P.; SLOVÁČEK, D. To performance modelling of virtual computers, In Proc.: TRANSCOM 2011 - section 3, pp. 213 – 216, 2011, Žilina [6] HUDIK, M. HANULIAK, P. Analysing Performance of Parallel Algorithms for Linear System Equations, In Proc.: GCCP 2011, October 24-26, pp. 70-77, 2011, SAV Institute of Informatics, Bratislava [7] JANOVIČ, F.; HOLÚBEK, A. Load balance and data decomposition for distributed prime number algorithm, In Proc.: TRANSCOM 2011, pp. 99 - 101, 2011, Žilina, Slovakia [8] JANOVIČ, F. Modelovanie výkonnosti distribuovaných paralelných algoritmov, ICSC Leden 2012, Kunovice, Czech republic (in print) [9] KIRK, D. B.; HWU, W. W. Programming massively parallel processors, Morgam Kaufmann, 280 pages, 2010 [10] KUMAR, A.; MANJUNATH, D.; KURI, J. Communication Networking , 750 pp., 2004, Morgan Kaufmann [11] LILJA D. J., Measuring Computer Performance, 280 pages, 2005, University of Minnesota, Cambridge University Press, United Kingdom [12] PATERSON, D. A.; HENNESSY, J. L. Computer Organisation and Design, 912 pp., Morgan Kaufmann, 2009 [13] SLOVÁČEK, D.; HANULIAK, P. Analysis of computer performance, In Proc. MMK 2010, pp. 42-51, 2010, 6.-10 Prosinec, Hradec Králové, Czech republic [14] SLOVÁČEK, D. Modelovanie výkonnosti viacprocesorových paralelných systémov , ICSC Leden 2012, Kunovice, Czech republic (in print) [15] THAKUR, R.; RABENSEIFNER, R.; GROPP, W. "Optimization of Collective Communication Operations in MPICH," Int'l Journal of High Performance Computing Applications, (19)1:49-66, Spring 2005 ADDRESS Ing. Martin Húdik Žilinská univerzita v Žiline Fakulta riadenia a informatiky, katedra technickej kybernetiky Univerzitná 8215/1 010 26 Žilina e-mail: [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 55 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 56 PERFORMANCE MODELLING OF MATRIX PARALLEL ALGORITHMS Filip Janovič Žilinská Univerzita Abstract: With the availability of powerful personal computers, workstations and networking devices, the recent trend in parallel computing is to connect a number of individual workstations (PC, PC SMP) to solve computation intensive tasks in parallel way on connected class of workstations (NOW, SMP, Grid). Current trends in high performance computing (HPC) are to use networks of workstations (NOW, SMP) or a network of NOW networks (Grid) as a cheaper alternative to traditionally used massively parallel multiprocessors or supercomputers. The individual workstations could be so single PC (Personal computer) as parallel computers based on modern symmetric multicore or multiprocessor systems (SMP) implemented within workstation. Such actual parallel systems (NOW, Grid) are connected through widely used communication standard networks and cooperate to solve one large problem. Each workstation is threatened similarly to a processing element as in a conventional multiprocessor system. To make the whole system appear to the applications as a single parallel computing engine (virtual parallel system), run time environments such as OpenMP, MPI, Java are used to provide an extra layer of abstraction. To exploit the parallel processing capability of such cluster, the application program must be paralleled. To behaviour analysis we have to take into account most important overheads that have the influence to performance of parallel algorithms (architecture, computation, communication etc.). On real application example we demonstrate the various influences in process of modelling and performance evaluation and the consequences for real parallel implementations. Keywords: complexity, parallel algorithm, performance modelling, network of analytical model, communication system, decomposition strategy workstations, 1. INTRODUCTION There has been an increasing interest in the use of networks of workstations (Cluster) connected together by high speed networks for solving large computation intensive problems. This trend is mainly driven by the cost effectiveness of such systems as compared to parallel computer with massive number of tightly coupled processors and memories. Parallel computing on a cluster of powerful workstations (NOW, SMP, Grid) connected together by high speed networks have given rise to a range of hardware and network related issues on any given platform. Network of workstations (NOW) has become a widely accepted form of high-performance parallel computing. As in conventional multiprocessors, parallel programs running on such a platform are often written in an SPMD form (Single program – multiple data) to exploit data parallelism or in an improved SPMD form to take into account also the potential of functional parallelism of a given application. Each workstation in a NOW is treated similarly to a processing element in a multiprocessor system. However, workstations are far more powerful and flexible than processing elements in conventional multiprocessors. From the point of system classification we can divide parallel systems to the two mutual very different groups synchronous parallel architectures [4, 14, 16]. To this group belong practically all known parallel architectures except computer networks. The basic system properties are given through the existence of some kind of the common shared memory M by parallel processors P i. asynchronous parallel architectures [4, 16]. This group covers field of various forms of computer networks. Their basic property is the mutual interconnection both in the remote form of the distributed memory modules Mk and the parallel processors Pi with using the existed telecommunication lines (WAN networks) and in the local form in reaching range of the used fixed lines (LAN networks), respectively. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 57 2. PROPERTIES OF PARALLEL ALGORITHMS The load balancing, inter process communication and transport protocol for such machines are being widely studied [4, 9, 10]. With the availability of cheap personal computers, workstations and networking devises, the recent trend is to connect a number of such workstations to solve computation intensive tasks in parallel on such clusters. To exploit the parallel processing capability of a NOW, the application program must be parallelised. The effective way how to do it for a particular application problem (Decomposition strategy) belongs to the most important step in developing a effective parallel algorithm [5, 7, 15]. To choose the best decomposition method for these applications, it is necessary to understand the particular application problem, the data domain, the used algorithm and the flow of control in given application. Therefore, according to the character of given task the following decomposition models are used perfectly parallel decomposition domain decomposition control decomposition object oriented programming (OOP). 3. PERFORMANCE EVALUATION Quantitative evaluation and modelling of hardware and software components of the parallel systems are critical for the delivery of high performance. Performance studies apply to initial design phases as well as to procurement, tuning, and capacity planning analysis. As performance cannot be expressed by quantities independent of the system workload, the quantitative characterisation of application resource demands and their behaviour is an important part of any performance evaluation study. Among the goals of parallel systems performance analysis is to estimate the performance of a system or a system component or an application, to investigate the match between requirements and system architecture characteristics, to identify the features that have a significant impact on the application execution time, to predict the performance of a particular application on a given parallel system, to evaluate different structures of parallel applications. To the performance evaluation we briefly review the techniques most commonly adopted for the evaluation of parallel systems and its metrics. To the performance evaluation we can use following methods analytical methods [6, 8, 9, 10] application of queuing theory [3] Petri nets [11] order analysis [1, 2] simulation methods [11] simulation experiments benchmarks [12, 13] direct measuring of particular developed parallel application [4, 5, 6]. In order to extend the applicability of analytical techniques to the parallel processing domain, various enhancements have been introduced to model phenomena such as simultaneous resource possession, fork and join mechanism, blocking and synchronisation. Hybrid modelling techniques allow to model contention both at hardware and software levels by combining approximate solutions and analytical methods. However, the complexity of parallel systems and algorithms limits the applicability of these techniques. Therefore, in spite of its computation and time requirements, simulation is extensively used as it imposes no constraints on modelling. 3. 1. EVALUATION METRICS To evaluating parallel algorithms there have been developed several fundamental concepts. Tradeoffs among these performance factors are often encountered in real-life applications. 3.1.1. SPEED UP Let O(s, p) be the total number of unit operations performed by p processor system, s defines size of the computational problem and T(s, p) be the execution time in time units. Then speedup factor is defined as S ( s, p ) T ( s, 1) T ( s, p ) ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 58 3.1.2. EFFICIENCY The system efficiency for a p processor system is defined by E ( s, p ) S ( s, p ) T ( s, 1) p p T ( s, p ) 3.1.3. ISOEFFICIENCY CONCEPT We denote the workload w = w (s) as a function of size of the problem s. For parallel algorithms we define an isoefficiency function relating workload to machine size p needed to obtain a fixed efficiency E when implementing a parallel algorithm on a parallel computer. Let h (s, p) be the total overhead function involved in the parallel algorithm implementation. The efficiency of a parallel algorithm is defined as E ( s, p ) w( s) w( s) h( s, p) The workload w (s) corresponds to useful computations while the overhead function h (s, p) represent useless overheads times (communication delays, synchronisation, control of processes etc.). With a fixed problem size (Fixed workload), the efficiency decreases as p increase. The reason is that the overhead h(s, p) increases with p. With a fixed machine size, the overhead function h (s, p) grows slower as workload w does. Thus the efficiency increases with increasing problem size for a fixed-size machine. Therefore, one can expect to maintain a constant efficiency if the workload w is allowed to grow properly with increasing machine size (Scalability). 4. COMPLEXITY OF FUNCTIONS AND ORDER ANALYSIS Order analysis and the asymptotic complexity of functions are used extensively in practical applications to analyse the performance of algorithms. When analysing parallel algorithms in this book, we use the following three types of functions 1. Exponential functions: A function f from reals to reals is called an exponential function in x if it can be expressed in the form f (x) = ax for x, a (the set of real numbers) and a > 1. Examples of exponential functions are 2x, 1.5x+2, and 31.5x. 2. Polynomial functions: A function f from reals to reals is called a polynomial function of degree b in x if it can be expressed in the form f (x) = x b for x, b and b > O. A linear function is a polynomial function of degree one and a quadratic function is a polynomial function of degree two. Examples of polynomial functions are 2, 5 x, and 5.5 x2.3. A function f that is a sum of two polynomial functions g and h is also a polynomial function whose degree is equal to the maximum of the degrees of g and h. For example, 2x + x 2 is a polynomial function of degree two. 3. Logarithmic functions: A function I from reals to reals that can be expressed in the form f (x) = log b x for b and b > 1 is logarithmic in x. In this expression, b is called the base of the logarithm. Examples of logarithmic functions are log1.5 x and log2 x. Unless stated otherwise, all logarithms in this book are of base two. We use log x to denote log2 x, and log2 x to denote (log2 x)2. Most functions in this book can be expressed as sums of two or more functions. A function f is said to dominate a function g if f (x) grows at a faster rate than g(x). Thus, function f dominates function g if and only if f (x) / g (x) is a monotonically increasing function in x. In other words, f dominates g if and only if for any constant c > 0, there exists a value xo such that f (x) > c g (x) for x > xo. An exponential function dominates a polynomial function and a polynomial function dominates a logarithmic function. The relation dominates is transitive. If function f dominates function g, and function g dominates function h, then function f also dominates function h. Thus, an exponential function also dominates a logarithmic function. 4.1. ORDER ANALYSIS OF FUNCTIONS In the analysis of algorithms, it is often cumbersome or impossible to derive exact ex¬pressions for parameters such as run time, speedup, and efficiency. In many cases, an approximation of the exact expression is adequate. The approximation may indeed be more illustrative of the behaviour of the function because it focuses on the ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 59 critical factors influencing the parameter. The Notation: Formally, the notation is defined as follows: given a function g(x), f(x) = (g(x) if and only if for any constants c1, c2 > 0, there exists an x0 such that c1 f(x) g(x) c2 f(x) for all x x0. The O Notation: Formally, the O notation is defined as follows: given a function g(x), f(x) = O(g(x) if and only if for any constant c > 0, their exists an x0 0 such that f (x) c g (x) for all x x0. From this definition we deduce that DA(t) = O(t2) and DB(t) = O(t2). Furthermore, D A (t) = O (t) also satisfies the conditions of the O notation. The Notation: The O notation sets an upper bound on the rate of growth of a function. The notation is the converse of the O notation; that is, it sets a lower bound on the rate of growth of a function. Formally, given a function g (x), f (x) = (g (x) if and only if for any constant c > 0, there exists an x0 0 such that f(x) c g(x) for all x x0. 5. MODELLING OF COMPLEXITY IN PARALLEL ALGORITHMS To this time known results in complexity modelling on the in the world used classical parallel computers with shared memory (supercomputers, SMP and SIMD systems) or distributed memory (Cluster, NOW, Grid) mostly did not consider the influences of the parallel computer architecture and communication overheads supposing that they are lower in comparison to the latency of executed massive calculations [12]. In this sense analysis and modelling of complexity in parallel algorithms (PA) is rationalised to the analysis of complexity of own calculations, that mean that the function of control and communication overheads are not a part of derived relations for execution time T (s, p). In this sense the function in the relation for isoefficiency suppose, that dominate influence to the overall complexity of the parallel algorithms has complexity of performed massive calculations. Such assumption has proved to be true in using classical parallel computers in the world (Supercomputers, massively multiprocessors – shared memory, SIMD architectures etc.). To map mentioned assumption to the relation for asymptotic isoefficiency w(s) means that w ( s) max Tcomp , h ( s, p) Tcomp max Tcomp In opposite at parallel algorithms for the actually dominant parallel computers on the basis NOW (including SMP systems) and Grid is for complexity modelling necessary to analyse at least most important overheads from all existed overheads which are [5, 6, 8] architecture of parallel computer own calculations (Tcomp) communication latency (Tcomm) start - up time data transmission routing parallelisation latency (Tpar) synchronisation latency (Tsyn). Taking into account all this kinds of overheads the total parallel execution time is T ( s, p) complex Tcomp Tpar Tcomm Tsyn where Tcomp, Tpar, Tcomm, Tsyn denote the individual overheads for calculations, parallelisation overheads, communication and synchronisation overheads. The more important overhead parts build in the relation for isoefficiency the used the overhead function h (s, p), which influence in general is necessary to take into account in performance modelling of parallel algorithms. In general nonlinear influence of h (s, p) could be at performance parallel algorithm modelling dominant (Fig. 2.). Then for asymptotic isoefficiency analysis is true ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 60 w ( s) max Tcomp , h ( s, p) where the most important parts for dominant parallel computers (NOW, Grid) in overhead function h (s, p) is the influence of Tcomm (Communication overheads). Calculation time T (s, p)comp of parallel algorithm is given through quotient of sequential running time (Complexity product of sequential algorithm Zsa and a constant tc as a average value of performed calculation operations) through number of used calculation nodes of the given parallel computer. Parallel calculation complexity of T(s,p) as a limit of a theoretical unlimited number of calculation nodes is given as T ( s, p )comp lim p Z sa . tc 0 p Communication time T (s, p)comm is given through the number of performed communication operations in concrete parallel algorithm and depends from used decomposition model. To the practical illustration of communication overheads we used the possible matrix decomposition models. 5.1. DECOMPOSITION MATRIX MODELS In general we are considering the typical possible decomposition strategies in following matrix A= a11, a12, . . . , a 1n a21, a22, . . . , a 2n . . . . . . . . . am1, am2, . . . , a mn In order to achieve effective parallel algorithm it is necessary to map every parallel process more than one matrix element. Then for mapping a cluster of matrix elements there are in principal two ways mapping of square blocks to every parallel process as illustrated at Fig. 1 a) mapping of p columns or rows (for example according Fig. 1 b). Depending of used decomposition methods there are derived needed communication activities. In general square matrix in two dimensions in halts n2 elements (complexity for sequential algorithm, which are equally divided to p build parallel processes, that means every parallel process gets n2 / p elements. Communication consequences for mentioned decomposition methods illustrate Fig. 1. 5.1.1. MATRIX DECOMPOSITION TO BLOCKS For mapping matrix elements in blocks a inter process communication is performed on the four neighbouring edges of blocks, which it is necessary in computation flow to exchange. Every parallel process therefore sends four messages and in the same way they receive four messages at the end of every calculation step supposing that all needed data at every edge are sent as a part of any message). Then the requested communication time for this decomposition method is given as Tcomb 8 (ts n tw ) p This equation is correct for p ≥ 9, because only under this assumption it is possible to build at least one square because only then is possible to build one square block with for communication edges. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 61 n ... ... ... ... ... ... n/ p b) a) Fig. 1. Communication consequences a) blocks b) strips Using these variables for the communication overheads in decomposition method to blocks is correct T ( s, p )comm Tcomb h ( s, p ) 8 (ts n tw ) p 5.1.2. MATRIX DECOMPOSITION TO STRIPS Decomposition method to rows or columns (Strips) are algorithmic the same and for their practical using is critical the way how are the matrix elements putting down to matrix. For example in C language are array elements put down from right to left and from bottom to top (Step by step building of matrix rows). In this way it is possible send very simple through specification of the beginning address for a given row and through a number of elements in row (Addressing with indexes). Let for every parallel process (strips) two messages are send to neighbouring processors and in the same way two messages are received from neighbouring processors supposing that it is possible to transmit for example one row to one message. Communication time for a calculation step Tcoms is then given as Tcoms 4 ts n tw Using these variables for the communication overheads in decomposition method to strips is correct T ( s, p)comm Tcoms h ( s, p) 4 (ts n t w ) 5.1.3. ANALYSIS OF COMMUNICATION PARAMETERS Based on performed analysed used parallel computers in the world comes out that values t s have one or two ranks higher values as tw and essentially higher values as tc (for example for NOW type IBM SP-2 ts =35 µs, tw =230 ns, tc = 4,2ns). If for these values (IBM SP-2) we normalise a value tc (tc =1 time unit), then ts has a value 8 333 and tw 55 time units. From this comes out that ts>> tw > tc, that is a dominant influence of value ts of the given parallel computer. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 62 n=256 500 T [µs] 450 400 350 300 D1 250 D2 200 150 100 50 0 0 20 40 60 80 100 120 140 160 180 200 220 240 p 260 Fig. 2. The role of decomposition method. 5.2. DECOMPOSITION METHOD SELECTION For comparison based on derived relations for communication complexity decomposition method to blocks demands higher communication time as decomposition to strips (more effective decomposition to strips) if 8 (t s n tw ) 4 (t s n tw ) p or after adjusting (for p ≥ 9) ts n (1 2 ) tw . p Fig. 2. illustrates choice optimisation of suitable decomposition method based on derived dependences to establishing ts for n = 256 and values tw for NOW type IBM SP-2 (tw = 230 ns = 0,23 µs) and for one rank higher value tw = 2,4 µs (NCUBE-2) according Fig. 2. For higher values ts as at given tw (tw = 0,23 µs), tw = 2,4 µs) from a appropriate curve line for n = 256 is more effective decomposition method to strips. Limited values in choice optimal decomposition strategy are at given n for higher values t w higher. Therefore in general decomposition to strips is more effective for higher values of ts. 6. CONCLUSIONS The paper deals with the role of parallel complexity in parallel algorithms. Due to the dominant using of parallel computers based on the standard PC in form of NOW and Grid, there has been great interest in performance modelling of parallel algorithms in order to achieve optimised parallel algorithms (Effective parallel algorithms). Therefore this paper summarises the used methods for complexity analysis which can be applicable to all types of parallel computers (supercomputer, NOW, Grid). Although the use of NOW and Grid parallel computers should be in some parallel algorithms less effective than the used of massively parallel architectures in the world (Supercomputers) the parallel computers based on NOW and Grid belong nowadays to dominant parallel computers. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 63 REFERENCES [1] ARORA, S.; BARAK, B. Computational complexity - A modern Approach, Cambridge University Press, 573 pp., 2009. [2] GOLDREICH, O. Computational complexity, Cambridge University Press, 632 pages, 2010. [3] GELENBE, E. Computer system performance modeling in perspective, 288 pages, published September 2006, Imperial College Press. [4] HANULIAK, I.; HANULIAK, P. Performance evaluation of iterative parallel algorithms, Kybernetes, Volume 39, No.1, United Kingdom : 2010, pp. 107- 126. [5] HANULIAK, I.; HANULIAK, P. To performance modelling of parallel algorithms, ICSC 2011, sekcia č. 2, Kunovice : pp 125 - 132, Czech republic. [6] HANULIAK, P. Parallel iteration algorithms for Laplacean equation method, ICSC 2012, Kunovice : section 2, Czech republic (in print). [7] HANULIAK, P.; SLOVÁČEK, D. To performance modeling of virtual computers, In Proc.: TRANSCOM 2011 - section 3, Žilina : pp. 213 – 216, 2011. [8] HUDIK, M. Performance optimization of broadcast collective operation on multi-core cluster, ICSC Kunovice : Leden 2012, Czech republic (in print). [9] HUDIK, M.; HANULIAK, P. Analysing Performance of Parallel Algorithms for Linear System Equations, In Proc.: GCCP 2011, October 24-26, Bratislava : pp. 70-77, 2011, SAV Institute of Informatics. [10] HUDIK, M.; HANULIAK, P. Parallel complexity of linear system equation, In Proc.: TRANSCOM 2011 - section 3, Žilina : pp. 107-110, 2011. [11] KOSTIN, A.; ILUSHECHKINA, L. Modeling and simulation of distributed systems, 440 pages, Jun 2010, Imperial College Press. [12] KUMAR, A.; MANJUNATH, D.; KURI, J. Communication Networking, 750 pp., 2004, Morgan Kaufmann. [13] LILJA, D. J. Measuring Computer Performance, United Kingdom : 280 pages, 2005, University of Minnesota, Cambridge University Press. [14] PATERSON, D. A.; HENNESSY, J. L. Computer Organisation and Design, 912 pp., Morgan Kaufmann, 2009. [15] SLOVÁČEK, D.; HANULIAK, P. Analysis of computer performance, In Proc. MMK 2010, Hradec Králové : pp. 42-51, 2010, 6.-10 Prosinec, Czech republic. [16] SLOVÁČEK, D. Modelovanie výkonnosti viacprocesorových paralelných systémov, ICSC Kunovice : Leden 2012, Czech republic (in print). ADDRESS Ing. Filip Janovič, Fakulta riadenia a informatiky, Žilinská Univerzita ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 64 MATHEMATIC EVALUATION OF ECOTOXICITY TESTING Kateřina Kejvalová Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology Abstract: This article deals with problem of mathematic reliability of ecotoxicity testing. It describes reasons and methods of testing substances on live organisms and process of its evaluating. The main chapters are dedicated to one real test evaluated by standard methodand thenby an advanced statistic process. Conclusion of this article deals with comparison of those two methods . Key words: Ecotoxicity testing, EC50, inhibition, mathematic evaluation. INTRODUCTION Ecotoxicity testing is used to verify efficiency or dangerousness of those substances and agent, which can get into to environment – intentionally or by an accident. Methodology of the testing is described in various Czech, European or international standards (ČSN, EN, ISO). These standards are obligatory to obtain reliable results and to prevent redundant testing on animals and other live organisms [1]. There aretwo possibilities of testing according to the prescribed methodology. The first one is to state stimulation or inhibition of the agent diluted according to the recommended dosage. The second one is to find the value EC 50 - concentration or dosage of the agent that kills, immobilizes or reduces growth (inhibits) 50 % of organisms compared to the control sample (without any agent) [4]. The standards also prescribed organisms, which are used for testing. There are 4 basic organisms (daphnia magna, unicellular and fiber algae and sinapsisalba) and some others (fish, mouse, rat …). The methodology includes some basic mathematic operations but without any accuracy calculations or statistic testing. This article deals with statistic evaluation of EC 50 determination. For that are used real data from testing of influence of STOP-ALGIN (new developed algaecide agent) on sinapsisalba germination. STOP-ALGIN STOP-ALGIN is a new developed biocide agent produced by the company RAWAT consulting s.r.o. It is designated for extermination and prevention of algae, cyanobacteria and other undesirable organisms in industrial and technological systems and retention basins (e.g. water systems in power stations). METHODOLOGY OF TESTING ON THE SINAPSISALBA Sinapsisalba is an usual plant planted as “green fertilizer” or as the base ingredient for mustard. Also it is one of the organisms required for biocide agent testing. Its main advantage is very quick germination. For testing is necessary to use seed with certificated germination. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 65 Fig. 1. Sinapsis alba (http://www.biopix.info/white-mustard-sinapis-alba_photo-35560.aspx) The test is done in 5-grade diluting series (100 µl/l, 50 µl/l, 10 µl/l, 5 µl/l, 1 µl/l) corresponding with the recommended dosage in 3 or 5 repetitions. Constant volume (3 to 5 ml) of precisely diluted agent (diluted with special solution of nutrients in distilled water) is dropped on filtration paper in Petri dish. On that are exactly 20 seeds of sinapsisalba placed. The seeds germinate 72 hours in the dark (under aluminum foil) and then the length of all their roots is measured. In cause of 3 repetitions and 5-grade diluting series with 3 control samples it means 360 measurements. This high number guarantees satisfactory credibility of the testing. STANDARD DATA PROCESSING Is it to mention, that the methodology of testing is verified by many years of using so no statistic testing is required. Data processing is usually done by laboratory technicians and any “advanced statistic calculations” only increase professional image of the project. AVERAGE LENGTH OF THE ROOTS When all the roots are measured it is to calculate value of their average length in each concentration (average from 60 values). The results in single Petri dishes with the same concentration of the agent are not compared. Three of them are used only because of danger thatthe filtration paper in one of them would dry out. INHIBITION Inhibition describes how much some substance, agent etc. kills, immobilizes or reduces growth of tested organism compared to the control sample (without any tested substances). The opposite of inhibition is stimulation, when tested substance or agent helps to the organism to grow or reproduce. The inhibition is calculated with following formula (1) where is inhibition for the concentration , is the average root length in control solution, is average ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 66 root length for the concentration solution . 100 µl/l 50 µl/l 10 µl/l 5 µl/l 1 µl/l control 4,1 9,5 24,2 28,2 28,3 32,3 87,29% 70,59% 25,01% 12,51% 12,35% 0,00% average root length [mm] inhibition Tab. 1. Average length root length in single solutions and their inhibition EC50 As written above, the value EC50 is the concentration of the agent that kills or immobilizes 50 % of tested organism or reduces their growth by 50 % compared to the control sample (inhibition is 50 %) [10]. It is almost impossible to hit that concentration during testing so it is calculated by linear interpolation from two neighboring values. or (2) where is the calculated concentration (EC50), and are lower and higher concentrations in diluting series matching to and , which are inhibitions lower and higher than (required inhibition, in this case 50 %). The interpolation can be used only in case that concentrations and inhibitions of tested samples approximately linearly depend on each other, what can be calculated or verified by graph. Fig. 2. Linearity of inhibition (3) (4) STATISTIC VALUATION Although the methodology of ecotoxicity testing is verified by years of using is interesting to do some statistic calculation to get some knowledge about its accuracy and reliability. AVERAGE LENGTH OF THE ROOTS It is very easy to calculate the average value. But does it really represent the most probable value of all possible? And how accurate is it? The easiest way how to get some information about tested data is to state their standard ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 67 deviation. Than is possible to compare intervals of the most probable occurrence or to test the hypothesis, if those data belongs to the universe with expected distribution. single Petri dishes average standard relative length deviation deviation (mm) (mm) 100 µl/l 50 µl/l 10 µl/l 5 µl/l 1 µl/l 2,9 2,4 85% 5,5 5,5 101% 4,0 3,6 91% 10,6 8,4 79% 7,5 6,2 83% 10,4 7,5 73% 25,5 12,3 48% 25,4 9,1 36% 21,7 6,5 30% 29,5 14,7 50% 24,5 9,8 40% 30,7 14,8 48% 29,1 14,1 48% 20,3 15,9 78% 35,4 15,9 45% 32,9 16,7 51% 37,6 26,3 control 17,4 8,9 Tab. 2. 46% 34% average length (mm) Combined data standard relative deviation deviation (mm) 4,1 4,1 99% 9,5 7,4 79% 24,2 10,5 43% 28,2 14,2 50% 28,3 16,9 60% 32,3 16,3 50% Standard deviation of the average root length NORMALITY OF MEASURED DATA To verify that measured data belong to aggregate with defined distribution is used Pearson’s test of goodness to fit. This test can be used only for combined data, because needs “enough large” number of values. We suppose that the length of roots of sinapsis alba germinated in same conditions (same concentration of tested agent) has normal distribution with mean value equal to the average value and standard deviation equal to the estimated one. 100 µl/l j tj nj 1 1 17 -0,76 0,2226 0,2226 13,35 0,995 2 3 21 -0,27 0,3932 0,1707 10,24 11,310 3 5 8 0,22 0,5877 0,1945 11,67 1,154 4 7 3 0,71 0,7625 0,1748 10,49 5,344 5 ∞ 11 sum 60 kj ∞ fj pj npj 1,0000 0,2375 14,25 0,742 1 19,544 60 T= 5,991 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 68 50 µl/l j tj 1 6 26 -0,47 0,3200 0,3200 19,20 2,406 2 12 14 0,34 0,6322 0,3122 18,73 1,195 3 18 12 1,14 0,8735 0,2413 14,48 0,424 4 24 5 0,182 5 ∞ sum nj 3 kj fj pj npj 1,95 0,9743 0,1008 6,05 ∞ 1,0000 0,0257 1,54 60 1 60 pj npj 1,383 5,590 T= 5,991 10 µl/l j tj 1 10 6 -1,35 0,0883 0,0883 5,30 0,995 2 20 19 -0,40 0,3451 0,2568 15,41 11,310 3 30 22 0,55 0,7102 0,3651 21,91 1,154 4 ∞ 13 60 ∞ 5,344 j tj kj 1 12 5 -1,14 0,1265 0,1265 7,59 0,884 2 24 19 -0,30 0,3832 0,2566 15,40 0,842 3 36 21 0,55 0,7084 0,3252 19,51 0,113 4 48 10 1,39 0,9184 0,2100 12,60 0,537 5 ∞ 0,002 sum nj kj fj 1,0000 0,2898 17,39 1 60 19,544 T= 3,841 5 µl/l sum nj 5 ∞ fj pj npj 1,0000 0,0816 4,90 60 1 60 pj npj 2,380 T= 5,991 1 µl/l j tj nj 1 13 14 -0,90 0,1828 0,1828 10,97 0,837 2 26 15 -0,13 0,4466 0,2637 15,82 0,043 3 39 13 0,64 0,7376 0,2910 17,46 1,140 4 52 15 1,41 0,9202 0,1826 10,95 1,494 5 3 sum 60 kj ∞ fj 1,0000 0,0798 4,79 1 60 0,668 4,182 T= 5,991 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 69 control j tj 1 13 9 -1,18 0,1184 0,1184 7,10 0,507 2 26 13 -0,38 0,3504 0,2321 13,92 0,061 3 39 18 0,41 0,6609 0,3105 18,63 0,021 4 52 12 1,21 0,8876 0,2267 13,60 0,189 5 ∞ 0,234 sum nj 8 kj ∞ fj pj npj 1,0000 0,1124 6,74 60 1 Tab. 3. 60 T= 5,991 1,013 Use of the Pearson’s test Legend j number of the interval tj high extreme of the interval j nj number of values belonging to the class j kj fj pj n T , where is average length for the concentration C and is estimated standard deviation value of distribution function of normal normalized distribution for kj probability of occurrence of measured value in interval (t j-1; tj) total number of measured values testing criterion, , where m is number of classes From those results can be seen, that except of the first solution (100 µl/l) the values have the predicted distribution with risk of mistake 5 %. It is understandable that lengths close to zero can’t have normal distribution, because they can’t be symmetric. For that reason was histogram constructed and distribution function estimated as (5) Fig. 3. Histogram of the root length in the most concentrated solution Suitability of this function was verified again using Pearson’s test of goodness to fit. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 70 100 µl/l j 1 2 3 4 5 sum tj nj 1 3 5 7 ∞ 17 21 8 3 11 60 fj pj npj 0,2485 0,5756 0,7603 0,8647 1,0000 0,2485 0,3271 0,1847 0,1043 0,1353 1 14,91 19,63 11,08 6,26 8,12 60 Tab. 4. 0,293 0,096 0,858 1,697 1,021 3,965 T= 5,991 Use of the Pearson’s test COMPATIBILITY OF MEASURED DATA Next testing was processed to verify, that length of roots germinating in different Petri dishes but with came concentration of the agent are same or at least similar. For that were two methods used. The first one was using of the interval estimation the second one the Two-sample T2 test. The same testswere used to verify that results in single Petri dish and in combination of the three of them are compatible. INTERVAL ESTIMATION In this were intervals , where l is the average length of roots and s the standard deviation of this value, compared. The confidence coefficient 2 was used to keep the 95 % dependability. Fig. 4. Interval estimation As seen in the graph, except of the two solutions with the lowest concentration, the results between single Petri dishes are comparable. All single samples are comparable with their combination. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 71 TWO-SAMPLE T2 TEST This test is used to verify difference between mean values of two aggregates with normal distribution. The test uses following figure: (6) where and are the average values of the two aggregates, s their standard deviations, n and m numbers of values and d the difference. In this case we suppose that the difference is zero for both comparisons: two Petri dishes and single Petri dish and combination of three of them. If the absolute value of the parameter T is lower than , we can with α % dependability say that the two aggregates are comparable. 1–2 T (two P.D.), t=2,02 T (sing. P.D. and comb.), t=1,99 -1,933 1,3 100 µl/l 2 – 3 0,982 -1,2 3–1 1,177 0,1 1–2 50 µl/l 2 – 3 1,325 -0,6 -1,305 1,07 3–1 -0,099 -0,4 1–2 10 µl/l 2 – 3 0,029 -0,5 1,506 -0,5 3–1 -1,238 1,01 1–2 1,253 -0,3 2–3 -1,565 1,09 3–1 0,268 -0,7 1–2 1,855 -0,2 2–3 -3,000 1,85 3–1 1,325 -1,7 1–2 control 2 – 3 -0,864 -0,2 2,578 -1,2 3–1 -1,561 1,55 5 µl/l 1 µl/l Tab. 5. Two sample T2-test Results got from the Two-sample T2 test are, as seen in the table, completely comparable with thosefrom interval testing. Only two problems appear between Petri dishes 2 and 3 with the two lowestconcentrations. ACCURACY OF THE INHIBITION As written above the inhibition depends on the ratio between average root lengths in tested and control solution. (7) From this formula can be the standard deviation if the inhibition expressed as (8) Where mC and mO are the standard deviations of the average root lengths in solution with the concentration C and control solution. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 72 100 µl/l lC - average root length (mm) 4,1 50 µl/l 9,5 7,4 70,59 % 27 % 10 µl/l 24,2 10,5 25,01 % 50 % 5 µl/l 28,2 14,2 12,51 % 62 % 1 µl/l 28,3 16,9 12,35 % 69 % control 32,3 16,3 0,00 % 71 % Cconcentration Tab. 6. mC(mm) I mI 4,1 87,29 % 14 % Standard deviation of the average root length and Inhibition Those results are very interesting and hard to be interpreted. It seems that the inhibition accuracy decreases with the decreasing concentration. But how can be the standard deviation of control inhibition 71 %, when this value is set to be exactly zero? This question requires future sophisticated solution. ACCURACY OF THE EC50 As written above, the value EC50 is such a concentration of tested agent that inhibits 50 % of organisms in relation to the control solution. It is interpolated from the closest higher and lower values, if they comply with some specific conditions. (9) For easier calculation we set following. and (10), (11) (12) (13) With our data we obtain (14) (15) (16) (17) (18) (19) (20) (21) This result shows high unreliability of the value EC50 calculated from this data set. CONCLUSION Statistic methods can be used in many fields either scientific or not. In case of biotechnology or biology at all it is necessary to treat them with caution, because the biological material (organisms or their parts) is more variable ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 73 than any other. Results of bio-testing are reliable when all standards during its processing were abided. On the other hand this article shows that sometimes is usefulto verify data and the method of their processing to avoid their incorrect interpretation. ACKNOWLEDGEMENTS The author thanks to the company RAWAT consulting s.r.o. for space and material for proceeding of the ecotesting and especially to Ing. Petra Hemzová for valued advices and help. REFERENCE [1] 376/2001 Sb. - Vyhláška Ministerstva životního prostředí a Ministerstva zdravotnictví o hodnocení nebezpečných vlastností odpadů [2] ČSN EN ISO 6341 Jakost vod – Zkouška inhibice pohyblivosti Daphnia magna Straus (Cladocera, Crustacea) - Zkouškaakutní toxicity [3] ČSN EN 28692 Jakostvod – Zkouška inhibicerůstu sladkovodních řas Scenedesmussubspicatus a Selenastrumcapricornutum (ISO 8692; 1989) [4] MŽP (2007): Metodický pokyn ke stanovení ekotoxicky odpadů, věstník MŽP 4/2007 [Citováno 200811-24]. [5] KOUTKOVÁ, H. Pravděpodobnost a matematická statistika: základy teorie odhadu. Vyd. 1. Brno : Akademické nakladatelství CERM, 2007. 50 s. ISBN 978-807-2045-273. [6] KOUTKOVÁ, H. Pravděpodobnost a matematická statistika: základy testování hypotéz. Vyd. 1. Brno : Akademické nakladatelství CERM, 2007. 50 s. ISBN 978-807-2045-280. [7] KOUTKOVÁ, H.; MOLL, I. Úvod do pravděpodobnosti a matematické statistiky. 1. vyd. Brno : VUT, 1990. 140 s. [8] http://www.zupraha.cz/cs/Ekotoxicita-21.htm[cit.: 18. 1. 2011, 14:00] [9] http://www.mzp.cz/osv/edice.nsf/390334EFF595E8B9C1256FC000440F3C/$file/Z_12ekotoxicita.html [cit.: 18. 1. 2011, 14:00] [10] http://en.wikipedia.org/wiki/EC50[cit.: 18. 1. 2011, 14:00] [11] http://www.enviwiki.cz/wiki/Ekotoxicita [cit.: 18. 1. 2011, 14:00] ADDRESS Ing. Kateřina Kejvalová Institute of Geodesy Faculty of Civil Engineering Brno University of Technology Veveří 331/95 602 00 Brno Czech Republic [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 74 MANAGERIAL DECISION-MAKING: MEASURING AND MANIFESTATIONS OF RISKS Dusan Marcek Research Institute of the IT4 Innovations Centre of Excellence The Silesian University Opava, Bezruc Abstract: The paper is concerned with measuring and assessment of risk scenes in managerial decision-making. It builds upon the uncertainty of economic information, which is converted into the concept of risk scene expressed in terms of probability and using confidence intervals of the predicted quantities. The paper explains the relation of a degree of risk expressed by the classical information measure, bit, by the concept of confidence intervals, or possibly by the standard deviation. Key words: confidence interval, uncertainty, entropy, prediction models, neural networks, managerial decision, risk scene assessment 1 INTRODUCTION Managerial decision-making is a complex issue, the complexity of which is caused by many factors. One of the factors is the way of obtaining information and its credibility for decision-making and operating with them. Every piece of information which the manager has at their disposal is overcast with uncertainty or entropy, as rooted in information sciences. This phenomenon is present throughout the whole process of managerial decision-making. Managers often find themselves in difficult situation due to uncertainty in the decision-making process. They realize the responsibility they have for the consequences of their decisions. The only way of reducing uncertainty of the whole decision-making process is making the information which serves as the basis for making decisions more precise. There is no need to emphasise the fact that using suitable means of making information more precise facilitates decision-making. An important sphere of information necessary for management of economic processes on all managerial levels is the information about the future development of quantities expressed quantitatively, which is used to characterise the state and the development of the object or process. Evidence shows that it is possible to make this information more precise by a suitable choice and use of forecasting models based on statistical methods, soft computing and artificial intelligence methods. In comparison with the manager's expert estimates, these models based on statistical and soft computing methods or artificial intelligence methods are capable of providing information in the form of forecasts of quantities with an acceptable degree of uncertainty. The manager using these forecasts is able to make better decisions, i.e. such decisions whose risks in achieving targets are minimized. Mathematical statistics [6, 23] offers the theory of point estimates and confidence intervals. The manager can set and influence the span of these confidence intervals. The confidence interval indicates the span of possible values into which falls the future estimate of the forecasted quantity with the chosen probability defined by the manager. This way the limits of the possible future values are set. Point or interval estimates of the future values of various economic indicators are important for the strategic manager's decision-making. When determining information entropy in decision-making, it is useful to focus on how the confidence interval for the forecasted economic quantity can be made more precise, i.e. narrowed by using the forecasting model. A significant prerequisite for the application of such a model in management is that apart from the increased reliability of decision-making, the model output results in uncertainty reduction, which makes decision-making easier and less weighted with risk. The fact or statement that uncertainty reduction facilitates the manager's decision-making is not sufficient. The crucial factor is how specifically the entropy change manifests itself in the consequences of the decision. Not only will it be “easier” to make the decision, but more importantly the decision will be more effective in the long run. One of the approaches to understanding uncertainty in forecasting models is understanding it as the standard deviation σ of the forecasted quantity or process [16, 17]. The standard deviation as a degree of uncertainty, or risk, of forecasted quantity values estimates is equivalent to the statistical degree of accuracy of the forecast defined as Root Mean Square Error of the forecast [14 – 16]. This approach is used with measuring risks of prognoses of many economic and financial forecasting models, and in forecasting models of economic time ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 75 series, models for managing financial risk [11, 25, 26], methods based on the extreme value theory [19], and Lévy models [1, 2], methods to assess and control financial risk [12], methods based on time intensity models, usage copulas and implementing risk systems [3]. For management, the approach based on the statistical analysis of the dispersion of the quantity values, or on the standard deviation analysis, is the most comprehensible way of representing uncertainty. It need to be stated that the standard deviation does not reflect entropy in its true substance as uncertainty which is indicated in bits (binary digits). On the other hand, uncertainty is closely related to how precise are the estimates of the future values of quantities that managers have at their disposal. The less precise the estimate, the larger the standard deviation, and the higher the uncertainty that the information is weighted with. This view of uncertainty does not articulate it in its true sense, however, it expresses very well its inner essence and the mutual relation of entropy and decision-making. The objective of the paper is to point out specific outlines of uncertainty and risk categories, determine their content in managerial decision-making as a category which conditions the ways and methods of management not only at the stage of decision-making but also the impacts at the stage of implementation of the decision, where the consequences of these decisions (effects or losses) will manifest themselves. The aim of the paper is also to point out the direct relation between the amount of the removed uncertainty and the quality of the manager's decision. The issue of measuring risk in management and its accompanying phenomena is divided into four chapters in the present paper. Chapter two is devoted to characterizing risk and its manifestation in decision-making in uncertainty conditions. In the third chapter, a diagram of an uncertainty reduction procedure in the manager's decision-making is designed and characterized. In the fourth chapter, risk reduction with the use of forecasting models based on the classical (statistical) methods and models based on artificial intelligence is documented and assessed. Chapter five summarizes the main topics and results. 2 THE RLATION BETWEEN DECISION-MAKING WITH UNCERTAINTY AND DECISIO-MAKING WITH RISK Specific choice of tools and models for decision-making depends on whether the manager has precise and complete or imprecise and incomplete information at their disposal. The complexity of managerial decisionmaking relates to decision-making with incomplete information. Most of the real systems can only be described incompletely, i.e. with information which cannot be formally expressed by unequivocally set parameters. This is uncertain information then. In practice, according to [20], there are mainly two types of such information: According to the first type, uncertain information makes it impossible to exactly determine the future behaviour of the examined system. This type of uncertainty is called stochastic, and it can usually be modelled using the probability theory. Stochastic uncertainty is concerned with the category of the probability risk, which is determined as a scene in the future associated with the specific adverse incident that we are able to predict it using probability theory and a lot of data [10]. In this manuscript, we will concern with this type models, which may be described as follows. Let D be a managerial prediction system including explanatory variables V to explain the behaviour of the variable to be forecast, and faults represented as forecast errors et in time t = 1, 2,…n. A risk function R in term of the conceptual model D for having a risk scene can be represented as R D(V , et ), t 1, 2,...n (1) To assess the managerial prediction risk R we apply different forecasting models which parameters are estimated by statistical tools. The second type of uncertainty is connected with the description or formulation of the actual meaning of the phenomena or statements about them. This is semantic uncertainty. Natural language words semantics with uncertainty, i.e. with meanings of words and individual statements not being exact, is typical of natural language. This uncertainty has the character of possibility rather than probability, and it is most often modelled by fuzzy systems [5, 9, 13, 22, 24]. As far as decision-making with risk is concerned, this is the case of decision-making where actual information about real systems is uncertain, and it is not important if the uncertainty is caused by incomplete information about the system's behaviour, or if it is semantic uncertainty. In the further text, in ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 76 accordance with, the risk connected with managerial decision-making will be modelled using probability models and understood as a statistical term of the expected value between two extreme states of decision, i.e. with full uncertainty and decision with certainty. 3 THE ASSESSMENT OF UNCERTAINTY USING THE CONFIDENCE INTERVALS APPROACH As it was mentioned in the preceding chapter, within the managerial decision-making process uncertainty indicates the degree of risk of achieving targets. Information serves to the manager as the basis for their decisions-making. To minimize the decision risk, i.e. to minimize the negative impacts of the decision and to maximize the benefits of the individual decisions, it is extremely important to get to know the future state of the economic environment. Economic environment on the micro level is characterized by different economic. There are two ways in which the value of information for the manager is significantly increased. The first way is obtaining the sufficient amount of information in time and with the content that the manager can use for their decision-making. The second way is increasing the precision of the estimates of the future values of quantities and of the output of processes occurring in economy. Before making the decision itself, the manager must select a suitable forecasting model for determining the forecast. By selecting a suitable forecasting model according to the character of the monitored process, the manager can positively influence the quality of the forecast e.g. by increasing the precision of the prognosis. Because the classical forecasting models are based on the probability theory, it is obvious that these models are affected by stochastic uncertainty. It is natural that mangers try to obtain maximum utilizable information, i.e. the most precise values of the future estimate possible. For the assessment of the estimate uncertainty degree, the method of confidence intervals for point forecasts can be used. With determining forecast confidence intervals based on the classical forecasting models such as the models of regression analysis, exponential smoothing, and Winter's seasonal models is concerned e.g. A more complicated situation is in case of models based on artificial intelligence such as GMDH (Group Method of Data Handling) or the classical neural networks with adaptation of parameters by the gradient method using Back-propagation algorithm. In this case it is possible to test the H0 hypothesis of the expected type of probability distribution to determine confidence intervals provided that residuals have a normal probability distribution according to [7] , and this hypothesis can be verified using χ2 test of good fit on levels of significance set in advance. It is a wellknown, widely used and relatively universal method of mathematical statistics [6]. To obtain the correct result, it is necessary for the statistical data file to have at least 50 values. The H0 hypothesis, verified by applying the χ 2 test of good fit on the level of significance α = 0,01, claims that the residuals of the forecasted values from the actual values can be considered as a data file with a normal probability distribution. The span of the confidence interval is related to the estimate precision. The more precise the input from the forecasting model, the more precisely it is possible to set the span of the confidence interval, and the larger part of uncertainty is removed. Using the χ2 test of good fit, the H0 hypothesis can be verified on the level of significance α = 0.05 and α = 0.01, and this hypothesis claims that the residuals of the forecasted values from the actual values can be considered as a data file with a normal probability distribution. The confidence interval can be then calculated according to the following expression x x k . where k α n x n , x k . n (2) – the critical value of the standardized normal probability distribution, – the level of significance, σ is the standard deviation, – the length of the sample, – the expected value. Interesting about the support of the preference of forecasting models based e.g. on neural networks to managers' expert estimates in managerial decision-making is the information about the probability change. The calculation of this probability is possible from expression (2) as the level of significance k k x a n 1 est (3) where ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 77 α is the lower limit of the forecast interval of the prognosis calculated by forecasting model est is the estimate of the standard deviation According to the critical values of the standardized normal distribution, to k appertains a new . This implies that the probability that the mean value will fall into the narrower (more precise) interval will change from (1 – ). This begs the question, how will the entropy change if the estimate is more precise? The basic relation for entropy calculation is H (X) = − log2 P (X) (4) At present, one bit (binary digit) is used most often as the information unit. The information achieved in one information step, indicated in bits, means the choice of one of two possibilities, i.e. one step of a bivalent decision. The probability used in the relation for the calculation of entropy (4) is the probability that the estimate value will fall into the narrower 95% confidence interval. 4 ENTROPY AND STANDARD DEVIATIONS AS THE MEASURE OF UNCERTAINTY As we mentioned early, another measure of uncertainty used in the theory of information is entropy. According to [21] entropy and also uncertainty is expressed by the amount of information that we get after performing an experiment. For example, if we get a message that an event A has occurred with probability P(A), we also get information I(A) equal log 2 P( A) bit. In case the event A consists of a finite amount of measured events, i.e. subsets of probabilistic space while Ai A for i 1, 2,...n , n i 1 Ai and Ai Aj 0 for i j is valid, then the entropy expressed by Sannon´s definition is [21] n n i 1 i 1 H ( P) I ( Ai ).P( Ai ) I ( Ai ).log 2 P( Ai ) (5) In the introductory chapter, we mentioned the possibility of expressing or measuring uncertainty using the standard deviation. The standard deviation is used in literature as the degree of uncertainty and risk [4, 14]. As far as relevancy is concerned, it is probably the easiest and, for managerial practice, the most comprehensible way of expressing and quantification of uncertainty. While the entropy indicated in the information unit bit is at present a still relatively abstract and almost non-used measure for expressing risk in the sphere of managerial decision-making. Uncertainty in the sense of the standard deviation has a higher informative value for managers. Uncertainty expressed by the standard deviation has one drawback, which is unit incompatibility. Entropy is indicated in bits. Despite this fact, as we could see in the given examples, it is easier to work with entropy as the standard deviation. It is possible to state that reduction of entropy of the forecast system was achieved when its standard deviation of forecast errors was reduced. It can be clearly seen in expression (1). In technical systems, rule 3 σ is used which in the figurative meaning provides information about which interval the forecast will almost certainly fall into. Therefore, it provides certainty instead of uncertainty. But it is a certainty which will not push the manager forward with his decision-making if there is a big standard deviation. The real solution leading to the support of decision-making is reducing uncertainty of the forecast system by using a better forecasting model which will achieve lesser variability of prognosis errors. Described in [18], on the basis of prognosis errors analysis, is a method of searching for such a forecast horizon for which entropy and thus also prognosis risk is minimal. 5 CONCLUSION In managerial decision-making, risk is the central category based on which the effects of individual variants are assessed, and subsequently the final decision is chosen from several variants. In the present paper we showed the procedure of quantitative assessment of risk scene based on probability terms using confidence intervals for point estimates of economic quantities. We build upon measuring uncertainty based on information entropy ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 78 indicated in bits and on measuring based on prognosis confidence interval, where uncertainty is expressed in terms of the span of the confidence interval and the probability that by using forecasting model the set prognosis limits around the expected value will not be exceeded. Both approaches to measuring uncertainty were assessed from the viewpoint of utilization in managerial decision-making using forecasting models based on an expert estimate, statistical models, and neural networks models. In [8], the theory of this study is applied to forecasting models which are based on an expert estimate and a statistical theory, and the risk scenes are assessed in forecasting models based on neural networks. We showed that there are more ways of approaching the issue of measuring risk in managerial decision-making in companies. In [8] it was also proved that it is possible to achieve significant risk reduction in managerial decision-making by applying modern forecasting models based on information technology such as neural networks developed within artificial intelligence. Acknowledgement. This paper has been elaborated in the framework of the IT4Innovations Centre of Excellence project, reg. no. CZ.1.05/1.1.00/02.0070 supported by Operational Programme 'Research and Development for Innovations' funded by Structural Funds of the European Union and state budget of the Czech Republic. REFERENCES [1] APPLEBAUM, D. 2004. Lévy Processes and Stochastic Calculus, Cambridge: Cambridge University Press [2] BERTOIN, J. 1998. Lévy Processes of Normal Inverse Gaussian Type. Finance and Statistics 2:41-68 [3] BESSIS, J. 2010. Risk Management in Banking. New York: John Wiley & Sons Inc. [4] BREALY, R. A.; MYERS, S. C. 1984. Principles of Corporate Finance. Mc Graw-Hill Int. Book Company [5] BUCKLEY, J. J. 2005. Simulating Fuzzy Systems. Springer-Verlag, Berlin, Germany [6] COX, D.; HINKLEY, D. 1974. Theoretical Statistics. Chapman and Hall, London, UK [7] DA SILVA, A.P.; MOULIN, L. S. 2000. Confidence intervals for neural network based short-term load forecasting, Power Systems, IEEE Transactions, 15(4):1191-6 [8] FRANO, M. 2010. Lowering the entropy in managerial decision making using suitable prediction algorithms. Ph.D. Thesis, The University Press of Zilina, Zilina, Slovak Republic (in Slovak) [9] HUANG, C.F.; RUAN, D. 2008. Fuzzy risks and an updating algorithm with new observation. Risk Analysis 28 (3)681-94 [10] HUANG, C. F. 2009.A Note on the Difference between Disaster Prediction and Risk Assessment in Natural Disasters. New Perspectives on Risk Analysis and Crisis Response, vol 9, pp 1-7. Atlantis Press, Paris, France [11] JORION, P. 2006. Value at Risk. In: McGraw-Hill Professional Financial Risk Manager Hand¬book: FRM Part I/Part II. New Jersey: John Wiley & Sons, Inc [12] JORION, P. 2009. Financial Risk Manager Handbook. New Jersey: John Wiley & Sons, Inc. [13] KAHRAMAN, C.; KAYA, İ. 2009. Fuzzy process accuracy index to evaluate risk assessment of drought effects in Turkey. Human and Ecological Risk Assessment: An International Journal 15(4):789–10 [14] MARCEK, M.; MARCEK, D. 2008. Granular RBF Neural Network Implementation of Fuzzy Systems: Application to Time Series Modelling. Journal of Mult.-Valued Logic & Soft Computing 14:101-14 [15] MARCEK, M.; PANCIKOVA, L.; MARCEK, D. 2008. Ekonometrics and soft computing. The University Press of Zilina, Zilina, Slovak Republic (in Slovak) [16] MARCEK, M. 2009. Statistical and RBF NN models: Providing forecast and risk assessment. Central European Review of Economic Issues 12:175-82 [17] MARCEK, D.; MARCEK, M.; BABEL, J. 2009. Granular RBF NN Approach and Statistical Methods Applied to Modelling and Forecasting High Frequency Data. International Journal of Computational Intelligence Systems, 2-4:353-64 [18] MARCEK, D.; MARCEK, M.; MATUSIK, P. 2010. High Frequency Data: Making Forecasts and Looking for an Optimal Forecasting Horizon. Proc. of the IEEE 2010 Sixth International Conference on ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 79 [19] [20] [21] [22] [23] [24] [25] [26] NATURAL COMPUTATION – ICNC 2010, Vol. 4, Yantai, Chandong, China 10-12 August 2010, Ed. Shigang Yue et al, 1686-91 MEDOVA, E. A.; KRIACOU, M. N. 2001. Extremes in operational risk management. Working Paper. University of Cambridge OLEJ, V. 2003. Modelling of Economic Processes Based on Computational Intelligence. The University Press of Pardubice, Pardubice, Czech Republic (in Slovak) PALUCH, S. 2008. Theory of Information. The University Press of Zilina, Zilina, (in Slovak) Republic. URL: http://frcatel.fri.uniza.sk/esers/paluch/ti.pdf (in Slovak) TAH, J. H. M.; CARR, V. A. 2000. Proposal for construction project risk assessment using fuzzy logic. Construction Management and Economics 18:491-00 WEISBERG, S. 1980. Applied Linear Regression. Wiley, New York, USA WU, C. W. 2009. Decision-making in testing process performance with fuzzy data. European Journal of Operational Research 193(2):499-09 ZMESKAL, Z. 2005. Value at risk methodology under soft conditions approach (fuzzy-stochastic approach. European Journal of Operational Research 161:337-47 ZMESKAL, Z. 2005. Value at risk methodology of international index portfolio under soft conditions (fuzzy-stochastic approach). International Review of Financial Analysis 14:263-75 ADRESS: Prof. Ing. Dušan Marček, CSc. Research Institute of the IT4 Innovations Centre of Excellence The Silesian University Opava, Bezruc Square 13, 746 01 Opava, Czech Republic e-mail: [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 80 TESTING OF TOPCON GRS-1 INSTRUMENT USING RTK METHOD Irena Opatřilová1, Dalibor Bartoněk2 1 Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, 2 Evropský polytechnický institut, s.r.o., Kunovice Abstract: The paper deals with testing of Topcon GRS-1 instrument, specifically with evaluating of the position and height of a point in the good horizon, i.e. better than 75 %. The GRS-1 device is GNSS receiver, which is especially designed for GIS applications that are usually associated with single frequency code measurements using an internal antenna. In this case, we expect dm accuracy associated with the method of DGNSS. Nevertheless, the usage of this device is wider, because we can use an external antenna for determining the spatial position and use dual-frequency phase RTK measurements with cm accuracy. RTK method may be associated with the use of networks of permanent reference stations and this method. The article describes the preparation for testing in the form of reconnaissance and selection 10 points for measurement. Then it evaluates the testing method of RTK, in which the services of a Czepos network of permanent stations (RTK, MAX, RTK-PRS) and the services of a TopNET network (RTK, VRS-NVR3) have been used. The test results in this paper are interpreted using the graphs for some selected points, and also the tables with the average results of measurement for each service. Then there is the expected accuracy declared by the manufacturer that is compared with the obtained precision by testing and comparing the accuracy of services of a Czepos network. Keywords: Testing of GNSS receiver, RTK, network of permanent reference stations INTRODUCTION Nowadays there are many instruments for various applications related to satellite determining of the spatial position. The range of these devices can be divided for example to their accuracy. On the one hand there are instruments to evaluate the position with cm accuracy; on the other hand, there are devices with accuracy in the order of several meters. The instruments for surveying purposes belong to the first group of devices. These instruments may determine the points with mm accuracy using long observation and the subsequent post-processing. RTK method is used for of determining of the position in real time and this method is widely used in geodesy, in civil engineering and in other applications. The accuracy of this method is in the order of centimeters and a great advantage over the static method is immediate information about the position of the point. The static and RTK method determinate the position of point using the phase measurement. The devices used for GIS applications are another group of GNSS instruments. The position of points is usually determined using code measurement based on DGNSS method, which achieves dm accuracy. Phase and code measurements evaluate so-called the relative position of the point. It means that first a spatial vector is evaluated between the determined and known point and then the spatial coordinates of determined point are calculate from this vector. This method is more accurate than the so-called autonomous determination of position, in which the coordinates of points are derived only from the measured data using device itself. So the reference station is needed for relative determination of point. This station has the known coordinates of the point and measures at the same time as the device on the determined point (the rover). Such a reference station can be either our other apparatus, or the data from networks of permanent reference stations can be use. Nowadays three such networks are in the Czech Republic, which cover the whole territory of our country. It is a Czepos network operated by the Czech Office for Surveying, Mapping and Cadastre (COSMC) [3], a TopNET network by Geodis Brno [4] and a Trimble VRS Now Czech network [5], which is managed by Geotronics Praha. These networks provide more services. Either there are data from a particular station for subsequent post-processing, or services used for the RTK and DGNSS method. In the second case you need a mobile internet connection for receiving of correction data provided by individual services. The services for RTK are as follows. Either a customer chooses a particular reference station, from which it receives of correction data during measurement, or this station is searched itself. There are for example services called Czepos RTK and TopNET RTK. The second group is so-called the network ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 81 solution, in which mostly a virtual reference station is generated. The necessary corrections are subsequently received from this station. This group includes services called Czepos PRS, TopNET VRS and other. For example a list of services provided by a Czepos network is in Figure 1. Fig. 2 Topcon GRS-1[7] Fig. 1 The services provided by a Czepos network [6] The paper deals with testing of Topcon GRS-1 instrument, specifically with evaluating of the position and height of a point in the good horizon, i.e. better than 75 %. RTK method was used for the testing of instrument. It was worked with an external PG-A1 antenna during measuring, thanks to which we can determine the spatial position using dualfrequency measurements with cm accuracy. The device further includes an internal antenna for code measurements with dm accuracy, an internal GSM/GPRS modem, 2.0 Mpix digital camera, a electronic compass and is equipped with TopSURV software. More information about the device GRS-1 is shown for example in [7]. Fig. 3 The scheme of workflow during the testing of instrument The scheme of whole work progress during the testing of device is suggested in Figure 3. The services of a Czepos network (RTK, MAX, RTK-PRS) and a TopNET network (RTK VRS-NVR3) were used for the RTK measurement. The main goal of this work was not only the testing of selected device but also to familiarize with a particular type of GNSS receiver, with select services of networks of permanent reference stations, then to design the methodology of ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 82 measurement, to evaluate the accuracy of the instrument from measurement results, to compare it with the expected accuracy and to assess the use of this instrument in practice. TESTING OF INSTRUMENT SELECTION OF SUITABLE POINTS FOR TESTING At the beginning to select appropriate geodetic points for testing was necessary. 46 points of fundamental horizontal control were reconnaissanced. These points have known coordinates in S-JTSK system (Datum of Uniform Trigonometric Cadastral Network), altitude in Bpv system (Baltic Vertical Datum - After Adjustment) and also ETRS coordinates and ellipsoidal height. 41 points were found. 10 point from these were chosen for testing purposes so that they were evenly distributed throughout the Brno city, they had a horizon greater than 75 %, they were at different distances from the reference stations and an easily accessible by public transport was to them. Figure 4 shows the location of selected points within the city of Brno. Fig. 4 The selected geodetic points for testing RTK MEASUREMENT The external Topcon PG-A1 antenna (Fig. 5) was used for RTK testing. This antenna was placed on a tripod so that the influence of centering was as low as possible. The sample of measurement is in Figure 6. PG-A1 antenna is a dualfrequency and dual-constellation. It means that antenna receives signals from GPS and also from GLONASS. It was designed with the technology to eliminate errors caused by multipath [8]. Fig. 5 Dual-frequency and dual-constellation Topcon PG-A1antenna [9] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 83 Fig. 6 The sample of RTK testing The measurement was done on a 10 selected points in two periods. A point was measured at one period 30 times for each service separately. One measurement was imposed as the average of the 5 epochs. One epoch had a length of 1 second. It means that 150 measurements were made on every point during one period (5 services over a 30 measurement). Services used for RTK measurements were as follows: 1 - Czepos RTK 2 - TopNET RTK 3 - Czepos PRS 4 - TopNET VRS-NVR3 5 - Czepos VRS-MAX. The periods were separated from each other so that repeated measurements on individual points have been distinguished from each other at least 3 hour interval. The first period took place 9/26/11 and 9/28/11, the average number of satellites was 7+6 (GPS+GLONASS) and it was cloudy and about 23° C. The second period was 09/28/11 and 30/09/11, while the average number of satellites was 8+6, it was clear weather again about 23° C. The mask angle was 12° in both cases. PROCESSING OF RTK S-JTSK coordinates and Bpv elevation were exported into TXT format. All other measurement was processed in Microsoft Office Excel software. The measurements are processed separately for each point and for each period and formulas from [1] and [2] were used for computing. The average coordinates of a point in S-JTSK for individual services were calculated by the (1), and these were compared with coordinates given by the (2). 30 lj l i 1 i 30 j X lj , l is measured quantity, it means x and y coordinates and elevation of point i (number of measurement) = 1, 2, …, 30, j (number of service) = 1, 2, 3, 4, 5 (1) , X is given coordinate, possibly elevation of point (2) The measured and given coordinates were entered into the graph (Fig. 7), as well as the average values of measured coordinates for each service. Graphs have mm resolution. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 84 Fig. 7 The graph with results of 1st and 2nd period of RTK measurement on point 1 for individual services, the positional component Fig. 8 The graph with results of 1st and 2nd period of RTK measurement on point 8 for individual services, the height component ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 85 Similarly the height variations were calculated, which were represented for better clarity in the graphs (Fig. 8). Then mean errors of the differences of the measured coordinates from given coordinates (m) were calculated for individual service, again for both periods separately. 30 mj (3), (4) i 1 2 i , i li X where 30 Later the average value of the differences of the measured coordinates from given coordinates were calculated. They were determined for each service from all points and results are listed in the following table. ΔY,X was calculated using the formula: Y , X 2X 2Y (5) Average of the 1st period Average of the 2nd period Average of periods S-JTSK coordinate a Bpv elevation S-JTSK coordinate a Bpv elevation S-JTSK coordinate a Bpv elevation ΔY [m] ΔX [m] ΔH [m] ΔY [m] ΔX [m] ΔH [m] ΔY [m] ΔX [m] ΔY,X [m] ΔH [m] 1 0,005 -0,006 0,016 0,003 -0,007 0,014 0,004 -0,006 0,007 0,015 2 0,008 -0,006 0,015 0,010 -0,008 0,014 0,009 -0,007 0,011 0,015 3 0,005 -0,007 0,019 0,002 -0,010 0,019 0,004 -0,008 0,009 0,019 4 0,004 -0,005 -0,003 0,007 -0,009 0,016 0,005 -0,007 0,009 0,006 5 0,003 -0,007 0,014 0,001 -0,008 0,016 0,002 -0,007 0,008 0,015 Service Tab. 1 Testing of RTK – The average values of the differences between measured and given coordinates of points for individual services Then the average values of mean errors of these differences were calculated, i.e. the differences between the measured and given coordinates of points for each service (see Table 2). Average of the 1st period Average of the 2nd period Average of periods S-JTSK coordinate a Bpv elevation S-JTSK coordinate a Bpv elevation S-JTSK coordinate a Bpv elevation mY [m] mX [m] mH [m] mY [m] mX [m] mH [m] mY [m] mX [m] mY,X [m] mH [m] 1 0,010 0,010 0,026 0,010 0,010 0,032 0,010 0,010 0,010 0,029 2 0,011 0,010 0,031 0,012 0,013 0,031 0,012 0,011 0,012 0,031 3 0,011 0,013 0,040 0,011 0,018 0,038 0,011 0,015 0,013 0,039 4 0,018 0,011 0,046 0,011 0,013 0,033 0,015 0,012 0,013 0,039 5 0,009 0,010 0,029 0,011 0,013 0,031 0,010 0,012 0,011 0,030 Service Tab. 2 Testing of RTK – The average values of the mean errors of the differences between measured and given coordinates of points for individual services Here mY,X indicates the mean coordinate error calculated by the formula: mY , X mX2 mY2 2 (6) The accuracy of phase RTK measurement is stated by the manufacturer for the Topcon GRS-1 device as value My,x 10 mm+1,0 ppm (* base length) for the positional component and Mh 15 mm+1,0 ppm (* base length) for the height component [7]. These values were compared with average values of mY,X and mH for individual services at all points. The base length between the permanent station and the point (above which the device was) had to be determined. The length was calculated from given coordinates in the case of Czepos RTK a TopNET RTK services, for other services the length was selected as permanent value of 5 km. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 86 Tab. 3 Comparison of the achieved accuracy of phase RTK measurement with the accuracy provided by the manufacturer (for one multiple of M error) The results are in Table 3. The achieved accuracy was satisfactory for one multiple of mean error (M) in 66 % of the results for the positional component and in 30 % of the results for height component. 3 multiple of the error (M) was exceeded in three cases, namely by the height component. COSMC indicates on its website an overview of the results of testing the accuracy of the Czepos services and products [10, 11]. The mean errors of one measurement calculated from the differences of measured and given coordinates are given in Table 4. Czepos Service mxy [m] mh [m] RTK RTK-PRS VRS-MAX 0,014 0,013 0,010 0,045 0,044 0,039 Tab. 4 Czepos services – The mean errors of one measurement calculated from the differences of measured and given coordinates It is clear by comparing of these values with the values given in Table 2 that our measurement reached satisfactory accuracy. Unfortunately a TopNET network do not have any such specific information about the accuracy of their services on its website. CONCLUSIONS This paper describes testing of GNSS instrument, Topcon GRS-1, and some selected services provided by networks of permanent reference stations. The work is divided into three steps. In the first part a reconnaissance of terrain was done in which it was selected 10 points suitable for subsequent testing of device. The second part deals with the measurement using the RTK method, in which benefited from the services of a Czepos network (RTK, MAX, RTK-PRS) and services of a TopNET network (RTK, VRS-NVR3). There were no major complications during the measurements. The last part concerns the processing of measurements, from which the following results are known. All services achieve similar results, which are listed in Tables 1 and 2. Tables describe the average results of all ten points for the differences between measured and given coordinates and their mean errors. From these tables can be evaluated that Czepos RTK service had the best overall results in comparison with other services. Czepos MAX got an imaginary second place, TopNET RTK was the third, TopNET VRS-NVR3 reached the forth place and Czepos PRS had the worst results in comparison with other services. For all that the differences between the results of these services were not particularly significant. The achieved accuracy for mean errors of differences between measured and given the coordinates of points was compared with the accuracy provided by the manufacturer for RTK measurements (Table 3). The evaluation showed that 66 % of the measurement results for the positional component and 30 % of the results for the height component are in interval of one multiple of expected accuracy. 3 multiple of the expected accuracy was exceeded in three cases out of a hundred, namely all for the height component. The results for services of a Czepos network from Table 2, i.e. the results for the mean error of differences between measured and given coordinates, were compared with the accuracies, which Czepos introduces on its ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 87 website. Our measurements amounted to an overall better accuracy. The Topcon GRS-1 device is especially designed for GIS applications. For work, in which the user would be sufficient to determine the spatial position of the point with dm accuracy, can clearly recommend using code measurements taken by the internal antenna + a correction data from a network of permanent reference stations. This may include for example evidence of object for database of municipal offices (containers, bus stops, poster areas, etc.). If the user wants to determine the points with cm accuracy must already use an external antenna. Using it may be for example for mapping purposes in geodesy, in cadastre of real estate’s for renewal of cadastre documentation, in engineering surveying for quick setting-out, etc. Another great area of use is also forestry, water management, traffic engineering, archeology and more. In simple terms, the area of applications for this device is wide. REFERENCES [1] HAMPACHER, M.; RADOUCH, V. Teorie chyb a vyrovnávací počet 10. Praha : Vydavatelství ČVUT. 2003. 159 pages. ISBN 80-01-02833-X. [2] VILÍMKOVÁ, M. Testování sítě CZEPOS (Master thesis). Praha : České vysoké učení technické v Praze, Fakulta stavební. 2006. 109 pages. [3] http://czepos.cuzk.cz/_index.aspx, 4.12.2011 [4] http://topnet.geodis.cz/topnet/, 4.12.2011 [5] http://www.geotronics.cz/trimble-vrs-now-czech, 4.12.2011 [6] http://czepos.cuzk.cz/_servicesProducts.aspx, 3.12.2011 [7] http://obchod.geodis.cz/geo/grs-1-dualni-gis-prijimac, 3.12.2011 [8] http://obchod.geodis.cz/geo/antena-pg-a1, 3.12.2011 [9] http://www.topconuniversity.com/hardware/gnss-antennas/pga-1/, 3.12.2011 [10] http://czepos.cuzk.cz/_vysledky.aspx, 3.12.2011 [11] http://czepos.cuzk.cz/_vysledkyNS.aspx, 3.12.2011 ADRESS: Ing. Irena Opatřilová, Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, Veveří 331/95, 602 00, Brno, Czech Republic, phone: +420-541147221, [email protected] Assoc. prof. Dalibor Bartoněk, EPI, s.r.o. Kunovice, Osvobození 699, 686 04 Kunovice, Czech Republic, phone: +420-605912767, [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 88 QUANTUM MODEL OF ATOMS Ošmera Pavel EPI, s.r.o. Kunovice Brno University of Technology, Czech Republic Abstract: This paper is an attempt to attain a better model of the atomic nucleus using vortex-ringfractal models. The aim of this paper is the vortex-ring-fractal modelling of atoms, which is not in contradiction to the known laws of nature. We would like to find some acceptable models of the atomic nucleus. Our imagination is that the atomic nucleus consists from the ring protons and the ring neutrons. We present here computer calculations and pictures. Keywords: vortex-ring-fractal modelling, hydrogen atom, quantum, ring structures, vortex, fractal 1. INTRODUCTION The electrical force decreases inversely with the square of distance between charges. This relationship is called Coulomb’s law. There are two kinds of “matter”, which we can call positive and negative. Like kinds repel each other, while unlike kinds attract – unlike gravity, where only attraction occurs. When charges are moving the electrical forces depend also on the motion of charges in a complicated way (Feynman et al., 1977). Most of our knowledge of the electronic structure of atoms has been obtained by the study of the light given out by atoms when they are exited. The light that is emitted by atoms of given substance can be refracted or diffracted into a distinctive pattern of lines of certain frequencies and create the line spectrum of the atom. The careful study of line spectra began about 1880. The regularity is evident in the spectrum of the hydrogen atom. The interpretation of the spectrum of hydrogen was not achieved until 1913. In that year the Danish physicist Niels Bohr successfully applied the quantum theory to this problem and created a model of hydrogen. Bohr also discovered a method of calculation of the energy of the stationary states of the hydrogen atom, with use of Planck’s constant h. Later in 1923 it was recognized that Bohr’s formulation of the theory of the electronic structure of atoms to be improved and extended. The Bohr’s theory did not give correct values for the energy levels of helium atom or the hydrogen molecule-ion, H2+, or of any other atom with more than one electron or any molecule. During the two-year period 1924 to 1926 the Bohr description of electron orbits in atoms was replaced by the greatly improved description of wave mechanics, which is still in use and seems to be satisfactory. The discovery by de Broglie in 1924 that an electron moving with velocity v has a wavelength λ=h/mev. The theory of quantum mechanics was developed in 1925 with the German physicist Werner Heisenberg. Early in 1926 an equivalent theory, called wave mechanics, was independently developed by Austrian physicist Ervin Schroedinger. Important contributions to the theory were also made by the English physicist Paul Adrien Maurice Dirac. The most probable distance of the electron from the nucleus is thus just the Bohr radius rB; the electron is, however, not restricted to this distance. The electron is not to be thought of as going around the nucleus, but rather as going in and out, in varying directions, so as to make the electron distribution spherically symmetrical (Pauling,1988). Basic vortex-ring structures ware described in: (Osmera, 2006, 2007a, 2007b, 2008a, 2008b, 2009, 2010, and 2011). The “ring theory” is supported by experiments in (Lim, 2011). Fractals seem to be very powerful in describing natural objects on all scales. Fractal dimension and fractal measure are crucial parameters for such description. Many natural objects have self-similarity or partial-selfsimilarity of the whole object and its parts. Fractal analysis has become one of the fundamental methods of the image analysis. Fractal dimension D and fractal measure K are the two characteristic values, which can be determined by fractal analysis. Fractal measure characterize the properties of surfaces and edges of image structure, whereas the fractal dimension shows the trends of surfaces and edges changes in relation to the details of structures themselves. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 89 2. THE MODEL OF HYDROGEN WITH A LEVITATING ELECTRON The new model of the hydrogen atom with a levitating electron was introduced in (osmera, 2008b). There is attractive (electric) force F+ and (magnetic) repellent force F- : F F F e2 4 o 1 d o2 2 4 d d (1) electron proton d Fig.1. The levitating electron in the field of the proton (the fractal structure model of hydrogen H is simplified (Osmera, 2010). The hydrogen atom can have the electron on left side or on right side (Osmera, 2007a). The attractive force F+ is Coulomb’s force. The repellent force F- is caused with magnetic fields of the proton and the electron (see Fig.1). A distance between the electron and the proton is d. The electron moves between point d1 and point d2 .The energy Ei required to remove the electron from the ground state to a state of zero total energy is called ionization energy. The energy of the hydrogen atom in the ground state is E= – 13.6 eV. The negative sign indicates that the electron is bound to the nucleus and the energy 13.6 eV must be provided from outside to remove the electron from the atom. Hence 13.6 eV is ionization energy Ei for hydrogen atom. Calculation of ionization energy was introduced in (Osmera 2008b): proton covalent bond 2 electrons Fig. 2. Vortex-fractal ring structure of the hydrogen molecule ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 90 subelectron Fig. 3. Vortex-fractal ring structure of neutron (the electron is inside of the proton) neutron electron proton Fig.4. Vortex-fractal ring structure of the helium atom Electric lines are perpendicular to magnetic lines. Electric lines create complex coil structure. Electric lines create coil-ring structures that consist from coil sub-structures. It is coil-semi-fractal structure. Every neighbour coil structure consists from opposite rotated electric lines that repel each other. They are created from electron or positron ring-sub-structures (-3e, -3υ) (Osmera, 2006). The proton has coil-semi-fractal structure and the electron has ring-semi-fractal structure. mg. line el. line Fig.5 One coil layer of the electromagnetic field of the electron ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 91 proton electron Fig.6 The structure of hydrogen with one layer of the electromagnetic field. It is necessary to use several simple rules. Only two protons and two electrons can be on the same axis inside the atom. Every proton can have only one levitating electron. Electrons on one axis have opposite spin. It is Pauli’s exclusion principle. To add new proton with different axis we use neutrons which hold protons in one structure. Protons and neutrons are connected with nuclear bond. Acknowledgements. This work has been supported by EPI Kunovice 3. CONCLUSIONS The exact analysis of real physical problems is usually quite complicated, and any particular physical situation may be too complicated to analyze directly by solving the differential equations or wave functions. Ideas as the field lines (magnetic and electric lines) are for such purposes very useful. A physical understanding is a completely nonmathematical, imprecise, and inexact, but it is absolutely necessary for a physicist (Feynman at al., 1977). It is necessary combine an imagination with a calculation in the iteration process. Our approach is given by developing gradually the physical ideas – by starting with simple situations and going on more and more complicated situations. But the subject of physics has been developed over the past 200 years by some very ingenious people, and it is not easy to add something new that is not in discrepancy with them. The vortex model of the electron was inspired by vortex structure in the PET-bottle experiment with one hole connector ($3 souvenir toy, Portland, Oregon 2004), our connector with 2 or 3 holes, and levitating magnet “levitron” (physical toy). The “ring theory” is supported by experiments in (Lim, 2011). Now we realize that the phenomena of chemical interaction and, ultimately, of life itself are to be understood in terms of electromagnetism, which can be explain by vortex-ring-fractal structure in different state of self-organization inside gravum (Osmera, 2009). Mass and energy are a form of the matter. They differ in the topology structures. Energy can be transformed, not created or destroyed. Dark energy is spread uniformly through space. It is everywhere. A variety of sources suggests that energy contributing to this flatness may be divided as follows: ordinary matter, 4 %; dark matter 23 %; dark energy 73 percent. Nature prefers simplicity, symmetry and “beauty”. Arrangement of electrons in the atom must reply the structure of nucleus. The electron in the classical theory is described by its mass, charge, flavor, and spin. There is no size and no structure for electrons and quarks. The fundamental laws of the subatomic world are laws of probability, not laws of certainty. Electrons occupy “shells” in atoms and do not cluster together in the lowest-energy state. This conclusion is required to account for the periodic table. Classical theory does answer the question: Why do antiparticles have to be counted as negative particles. In vortex-fractalring structures of antiparticles all their substructures rotate in opposite direction. Conservation laws are connected to principles of symmetry. The electron structure is a semi-fractal-ring structure with a vortex bond between rings. The proton structure is a semi-fractal-coil structure. The proton is created from electron subsubrings e -2 and positron subsubrings υ-2 which can create quarks u and d (Osmera, 2010). This theory can be called shortly “ring” theory. It is similar name like string theory. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 92 In the covalent bond is a pair of electrons which oscillate and rotate around a common axis. There are two arrangements of hydrogen: with a left and a right side orientation of the electron in their structure. Very important is symmetry and self-organization of real ring structures. 4. REFERENCES [1] FEYNMAN, R. P.; LEIGHTON, R. B.; SANDS, M. (1977). The Feynman Lectures on Physics, volume I, II, III Addison-Wesley publishing company. [2] LIM, T. T. (2011) archived at serve.me.nus.edu.sg/limtt/ [3] OSMERA, P. (2006). Vortex-fractal Physics, Proceedings of the 4th International Conference on Soft Computing ICSC2006, January 27, Kunovice, Czech Republic, 123-129. [4] OSMERA, P. (2007a). Vortex-ring Modelling of Complex Systems and Mendeleev’s Table, WCECS2007, proceedings of World Congress on Engineering and Computer Science, San Francisco, 152-157. [5] OSMERA, P. (2007b). From Quantum Foam to Vortex-ring Fractal Structures and Mendeleev’s Table, New Trends in Physics, NTF 2007, Brno, Czech Republic, 179-182. [6] OSMERA, P. (2008a). The Vortex-fractal-Ring Structure of Electron, Proceedings of MENDEL2008, Brno, Czech Republic, 115-120. [7] OSMERA, P. (2008B). Vortex-fractal-ring Structure of Molecule, Proceedings of the 4th Meeting Chemistry and Life 2008, September 9-11, Brno, Czech Republic, Chemické listy (ISSN 1803-2389), 1102-1108. [8] OSMERA, P.; RUKOVANSKY, I. Magnetic Dipole Moment of Electron, Journal of Electrical Engineering, No 7/s, volume 59, 2008, Budapest, Hungary, 74-77Osmera P. (2009). Vortex-ring fractal Structures of Hydrogen Atom, WCECS2009, proceedings of World Congress on Engineering and Computer Science, San Francisco, 89-94. [9] OSMERA, P. (2010). Vortex-ring-fractal Structure of Atoms, journal IAENG, Engineering Letters, Volume 18 Issue 2, 107-118, Advance Online Version Available:http://www.engineeringletters.com/issues_v18/issue_2/index.html [10] OSMERA, P. (2011). archived at http://www.pavelosmera.cz [11] PAULING, L. (1988). General Chemistry, Dover publication, Inc, New York. ADRESS: Prof. Ing. Pavel Ošmera, CSc. EPI Kunovice Osvobozeni 699, 686 04 Kunovice Brno University of Technology, Technicka 2, Brno, Czech Republic ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 93 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 94 RBF NEURAL NETWORK APPLICATIONS USING JNNS SIMULATOR Jindřich Petrucha Evropský polytechnický institut, s.r.o. Kunovice Abstract: The paper deals about using artificial neural network and the architecture RBF for time series data. The process of set up architecture is explai, the first part describes RBF function. . In the second part is explaining. Keywords: Neural network, JNNS, RBF architecture, time series, , neural simulator, training neural networks 1. INTRODUCTION The simulators of neural networks represent one of the options for the application of artificial intelligence for decision making. There is very often necessary to observe phenomena in the economic area , that are stochastic in nature, and it is very difficult to find exact solutions for the mathematical expression of the phenomena. For these areas are artificial neural network simulators suitable tool. Simulators with a variant of RBF (Radial Basis fuction) in the hidden layer, are suitable for use in the prediction of time series and other economic phenomena. Use in practice shows very good results in their application. The application requires to set certain parameters to during training process and during building the neural network architecture. Differences between the type of neural network MLP and RBF Similarities 1. They are both non-linear feed-forward networks. 2. They are both universal approximators. 3. They are used in similar application areas in practice. Differences between MLP and RBF 1) An RBF network has a single hidden layer, whereas MLPs can have any number of hidden layers. 2) RBF networks are usually fully connected, whereas it is common for MLPs to be only partially connected. 3) In MLPs the computation nodes (processing units) in different layers share a common neuronal model, though not necessarily the same activation function. In RBF networks the hidden nodes (basis functions) operate very differently, and have a very different purpose, to the output nodes. 4) In RBF networks, the argument of each hidden unit activation function is the distance between the input and the “weights” (RBF centres), whereas in MLPs it is the inner product of the input and the weights. 5) MLPs are usually trained with a single global supervised algorithm, whereas RBF networks are usually trained one layer at a time with the first layer unsupervised. 6) MLPs construct global approximations to non-linear input-output mappings with distributed hidden representations, whereas RBF networks tend to use localised non-linearities (Gaussians) at the hidden layer to construct local approximations. 2. PRINCIPLE RBF ARCHITECTURE RBF neural networks using three-layers architecture, where the first layer is used for data input and hidden layer contains nodes that have a transfer function with radial bases. During training the neural network is necessary for these nodes to find the centers and width, which affect the output value of the function. Very often used is used method K-means clustering to find the centers for centroids of the individual functions of neurons in the hidden layer. The output layer contains one neuron that represents the desired output function. The simulators uses the these steps for k-means algorithm: Random initialize centers of RBF function ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 95 a/ Create groups of data to each function centers b/ Input data Xi belongs cluster j ll Xi-Cj ll = min ll Xi-Cj ll c/ Find function centers d/ Repeat step 2, until there is no more changes in each cluster This method of processing for RBF neural network simulator SNNS is implemented by using the transfer function of neurons with RBF. For the processing of time series of input patterns is necessary to prepare these patterns into a text file and use this data in neural networks. Finding centers each RBF function is a matter of software simulator. When properly designed architecture achieves this type of neural network very good results. The parameters that should be made in the design of architecture are: Number of neurons in the hidden layer Number of neurons in the input layer Both these parameters affect the speed indications. When a large number of neurons in the input layer increases the complexity of the calculation of the centers of RBF naleení functions with the use clastrování. When large numbers of neurons in the input layers will become much more complicated pattern and is lost genralizace neural networks. Also there is a shortening of the length of time series on the size of neurons in the input vrsvě. These parameters should be tested by experience podobých examples in practice. Description of the experimental test To experiment with the type of RBF neural network we use economic time series, where each value will be the final hodnnoty shares. This data on the x axis represent individual days and the y-axis value of the shares from the date 12. 1. 2011 to 11. 1. 2012. Each value shares of ORCL (Oracle) are listed in Table 1. Date Open High Low Close Volume Adj Close 12.1.2011 31,22 31,23 30,94 30,95 33962200 30,66 13.1.2011 30,97 31,39 30,9 31,18 43411700 30,89 14.1.2011 31,02 31,34 30,94 31,25 37933800 31,01 18.1.2011 31,26 31,55 31,23 31,53 26972100 31,29 … … … … … … … 9.1.2012 26,9 27,12 26,66 27,03 38476800 27,03 10.1.2012 27,18 27,6 26,85 26,97 48974800 26,97 11.1.2012 26,99 27,1 26,75 26,89 30832300 26,89 Table 1. input raw data fo experiment Graphical representation of 249 stocks closing values is shown below figure 1. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 96 40 35 30 25 20 Řada1 15 10 5 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 9 106 101 116 111 126 121 136 131 146 141 156 151 166 161 176 171 186 181 196 191 206 201 216 211 226 221 236 231 246 241 256 1 0 Figure 1. closing data of shares ORCL For experiments with a neural network simulator SNNS was chosen variant Java (JNNS), which allows modifying the transfer function of the type of neuron RBF and implemented variants of calculations. This simulator is very detailed in the text file for patterns and can be created by external programs to handle this file. This method greatly simplifies the creation of an input file for testing, because each time you change the size of the input layer is to change patterns. In the case of a manual would be necessary to carry out a large number of operations due to human factors may carry error in the calculation. Figure 2. RBF architecture of neural networks The text file was created patterns using the PHP language and the input text file. This text file was created from the excel saving only close values After the connection we are able to browse table for the quote that we choose at the component yahoo. These data we use for learning neural networks. The same component we have to use at the end of architecture of neural network as a desired output. One of the most important parts is to create temporary window as a delayed layer with delayed inputs and we have to set up number of these inputs. Typically we choose from 4 to 15, but it depends on our experience with time series. In the example we used 5 neurons, but the parameter of the number of neuron we can change and try to optimize learning process. All components we ca see on the figure 2. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 97 Figure 3. sets of paterns in external file Figure 4. window of process training rbf neural network Other options for how learning RBF networks Another option is learning RBF networks using genetic optimization methods in the first learning phase, during which changes the layout of the center of each RBF functions. This can replace the K-means clustering algorithm genetic and increase the speed of learning in the first phase of training RBF neural networks. 3. CONCLUSION Using features in the architecture of RBF neural networks allows to improve the learning process, and these networks achieve betterresults in the approximation of time series. Using the simulatorrequires setting certain ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 98 parameters before the learning process,especially in terms of set the length of the input layer neural network architecture. This process is linked to external programsthat generate the input patterns into text files. LITERATURE: [1] MARRONE, P. JOONE JavaObject Oriented Neural Engine, The Complete Guide [online]. 2007 [cit. 2009-01-20]. Dostupný z WWW: <http://heanet.dl.sourceforge.net/sourceforge/joone/JooneCompleteGuide.pdf>. [2] A GUI Example [online]. 2005 [cit. 2009-01-20]. Dostupný z WWW: <http://www.jooneworld.com/docs/sampleEditor.html>. [3] DOSTÁL, P. Pokročilé metody analýz a modelování v podnikatelství a veřejné správě. Akademické nakladatelství CERM: Brno, 2008, ISBN 978-80-7204-605-8. [4] DOSTÁL, P. Neural Network and Stock Market, In Nostradamus Prediction Conference, UTB Zlín, 1999, s8-13, ISBN 80-214-1424-3. ADRESS: Ing. Jindřich Petrucha, PhD. Evropský polytechnický institute, s.r.o. Osvobození 699 686 04 Kunovice [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 99 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 100 OPTIMIZATION OF THE THROUGHPUT OF COMPUTER NETWORK Imrich Rukovansky European Polytechnical Institute Kunovice Abstract: This paper describes the application of Two-Level Transplant Evolution (TE) in computer network optimization. TE combines Grammatical Evolution (on the genotype level) with Genetic Programming (tree structures on the phenotype level). To increase the efficiency of Transplant Evolution (TE) the parallel Differential Evolution was added. Keywords: computer network; optimization of throughput; two-level trans- plant evolution 1. INTRODUCTION Modern methods to increase efficiency of computer networks comprise two main attributes, i.e. time needed for solution finding and number of suitable variants of topology. The limit of the throughput of computer network is based on the principles of clustering and using parallel evolutionary algorithms (PEA) [2], [8] –[10]. Cluster Analysis: different approaches (hierarchical and relational clustering, EM clustering, objective function based clustering, fuzzy clustering, density based clustering, special techniques) choice of a suitable distance measures, cluster validity for determining the number of clusters and for checking the consistency of clustering results, visualization techniques for clustering results, specific problems with high-dimensional data Methods of (evolutionary techniques) can also be used on the synthesis and optimal setting of an appropriate topology of computer networks. In the case of softcomputing methods (or more generally artificial intelligence) they can be applied on a few major levels of research and application like: All these problems can be defined like problems of optimization. The aim of this paper is to describe a new optimization method that can optimize the throughput of computer network. For this type of optimization a new method was created and we call it Two-Level Transplant Evolution (TLTE). This method allowed us to apply advanced methods of optimization, for example direct tree reducing of tree structure of control equation. The reduction method was named Arithmetic Tree Reducing (ART). For the optimization of control equations of general controllers it is suitable to combine two evolutionary algorithms. The main goal in the first level of TLTE is the optimization of the structure of general controllers. In the second level of TLTE the concrete parameters are optimized and the unknown abstract parameters in the structure of equations are set. The method TLTE was created by the combination of the Transplant Evolution method (TE) and the Differential Evolution method (DE). The Transplant Evolution (TE) optimizes the structure of the solution with unknown abstract parameters and the DE optimizes the parameters in this structure. The parameters are real numbers. The real numbers are not easy to find directly in TE without DE. Some new methods for evaluation of the quality of the found control equation are described here, which allow us evaluate their quality. These can be used in the case when the simulation of the computer network cannot be finished. The PGE is based on the grammatical evolution GE [5], where BNF grammars consist of terminals and nonterminals. Terminals are items, which can appear in the language. Non-terminals can be expanded into one or more terminals and non-terminals. Grammar is represented by the tuple {N,T,P,S}, where N is the set of nonterminals, T the set of terminals, P a set of production rules which map the elements of N to T, and S is a start symbol which is a member of N. For example, the BNF used for our problem is below: N = {expr, fnc} T = {sin, cos, +, -, /, *, X, 1, 2, 3, 4, 5, 6, 7, 8, 9} S = <expr> ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 101 and P can be represented as 4 production rules: 1. <expr> := <fnc><expr> <fnc><expr><expr> <fnc><num><expr> <var> 2. <fnc> := sin cos + * U3. <var> := X 4. <num> := 0,1,2,3,4,5,6,7,8,9 The production rules and the number of choices associated with them are in Table 1. The symbol U- denotes an unary minus operation. rule no 1 2 3 4 choices 4 6 1 10 Table 1: The number of available choices for every production rule There are notable differences when compared with [1]. We don’t use two elements <pre_op> and <op>, but only one element <fnc> for all functions with n arguments. There are not rules for parentheses; they are substituted by a tree representation of the function. The element <num> and the rule <fnc><num><expr> were added to cover generating numbers. The rule <fnc><num><expr> is derived from the rule <fnc><expr><expr>. Using this approach we can generate the expressions more easily. For example when one argument is a number, then +(4,x) can be produced, which is equivalent to (4 + x) in an infix notation. The same result can be received if one of <expr> in the rule <fnc><expr><expr> is substituted with <var> and then with a number, but it would need more genes. There are not any rules with parentheses because all information is included in the tree representation of an individual. Parentheses are automatically added during the creation of the text output. If the GE solution is not restricted anyhow, the search space can have infinite number of solutions. For example the function cos(2x), can be expressed as cos(x+x); cos(x+x+1-1); cos(x+x+x-x); cos(x+x+0+0+0...) etc. It is desired to limit the number of elements in the expression and the number of repetitions of the same terminals and non-terminals. 2. BACKWARD PROCESSING OF THE GE The chromosome is represented by a set of integers filled with random values in the initial population. Gene values are used during chromosome translation to decide which terminal or nonterminal to pick from the set. When selecting a production rule there are four possibilities, we use gene_value mod 4 to select a rule. However the list of variables has only one member (variable X) and gene_value mod 1 always returns 0. A gene is always read; no matter if a decision is to be made, this approach makes some genes in the chromosome somehow redundant. Values of such genes can be randomly created, but genes must be present. The Fig. 1 shows the genotype-phenotype translation scheme. The individual body is shown as a linear structure, but in fact it is stored as a one-way tree (child objects have no links to parent objects). In the diagram we use abbreviated notations for nonterminal symbols: f - <fnc>, e - <expr>, n - <num>, v - <var>. 3. TRANSPLANT EVOLUTION Transplant Evolution (TE) was inspired by biological transplantation. It is an analogy to the transplant surgery of organs. Every transplanted organ was created by DNA information but some parts of an ill body can be replaced by a new organ from the database of organs [3]. The description parts of individual (organs) in the database are ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 102 not stored on the level DNA (genotype). In Transplant Evolution (TE) every individual part (organ) is created by the translation of grammar rules similar to Grammatical Evolution (GE), but Transplant Evolution (TE) does not store the genotype and the grammatical rules are chosen randomly. The newly created structure is stored only as a tree. This is like Genetic Programming (GP). The Transplant Evolution algorithm (TE) combines the best properties of Genetic Programming (GP) [1] and Grammatical Evolution (GE) [4], [5], [8], [9], and [10]. The Two-Level Transplant Evolution (TLTE) in addition to that uses the Differential Evolution algorithm (DE). Optimization of the numerical parameters of general controllers in recurrent control equations of general controllers is a very difficult problem. We applied the second level of optimization by the Differential Evolution method (DE). The individuals in TE and TLTE are represented only by a phenotype in the shape of an object tree. During the initialization of population and during the creation of these phenotypes, similar methods are used as in GE. In Grammatical Evolution the numerically represented chromosomes are used. The codons of these chromosomes are used for the selection of some rule from a set of rules. In Transplant Evolution the chromosomes and codons are not used, but for the selection of some rule from a set of rules randomly generated numbers are used. These numbers are not stored in the individual chromosome. The new individuals in the population are created with the use of analytic and generative grammar and by using crossover and mutation operators. These operators are projected for work with the phenotype of an individual, similarly as in GP. Because the individuals of TE and TLTE are represented only by phenotype, it was possible to implement these advanced methods in the course of evolution: an effective change of the rules in the course of evolution, without the loss of generated solutions, a difference of probability in the selection of rules from the set of rules and the possibility of this changing during the evolutionary process, the possibility of using methods of direct reduction of the tree using algebraic operations, there is a possible to insert some solutions into the population, in the form of an inline entry of phenotype, new methods of crossover are possible to use, (for example crossover by linking trees) A. Initialization of individual The Original initialization algorithm GE uses forward processing of grammatical rules. In the Grammatical Evolution the method of crossover and mutation are made on the genotype level. The phenotype is created by a later translation of this genotype. This way of mutation and crossover does not allow the using of advanced method in crossover and mutation operators, which does not destruct the already created parts of the individual [3]. During the evolution of this algorithm the Backward Processing of Rules (BPR) [2] arose [4]. The BPR method uses gene marking. This approach has the hidden knowledge of tree structure. Due to the BPR the advanced and effective methods of crossover and mutation can be used. Anyhow the BPR method has some disadvantages. Due to these disadvantages the new method Transplant Evolution (TE) was created. The TE method does not store genotype information. The equation (1) is used for the selection of a rule from rules base. The advantage of TE is the possibility to use both types of grammatical processing (forward and backward) with the same results, because TE works only with the phenotype and the procedure of phenotype creation is not important. Some examples of forward and backward initializations are shown in Fig.1 and Fig.2. In column A are shown the randomly generated gene values. These values are not stored anywhere! The values are generated only when is necessary to select from more grammatical rules. In column B is shown the arithmetic operation. In column C is shown a state of rules translation, but it must be remembered that the translation rules is done at the tree (in the nodes of the phenotype). In column F is the order of operations. These numbers are used for a description of the tree nodes initialization order. The tree initialization is shown at column G. Each node of the tree in column G is described by a number in the form Step X-Y. In the Step X-Y, X represents the step in which the node was created. Y represents the step in which the node was fully initialized (after initialization all of its subnodes). As you can see, the finite tree structures are the same, but they have a different order of fully initialization. The generated numbers in column A were changed too. B Presentation of tree structures The phenotype representation of the individual is stored in the object tree structure. Each of nodes in the tree structure, including the sub-nodes, is an object that is specified by a terminal symbol and the type of terminal ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 103 symbols. All nodes are independent and correctly defined mathematical functions that can be calculated, e.g. the function x-3, is a tree structure containing a functional block (sub-tree). Creating the object tree is a key part of TE, which this method differs from other evolutionary algorithms. When the object tree is generated, similar methods to a traditional grammatical evolution are used. But the TE does not store the genotype, because the production rules are selected by randomly generated genes that are not saved in chromosomes of individuals. The final TE’s individual contains only phenotype expressed in an object tree structure. The algorithm of TE uses a generative grammar [4], [5], [6] whose translation process starts from the initial symbol S and continues randomly with using the rules of defined grammar [2]. The basic procedure of the translation algorithm is shown on Fig. 4 where is explain to why is unnecessary to store the genotype. C Crossover The crossover is a distinctive tool for genetic algorithms and is one of the methods in evolutionary algorithms that are able to acquire a new population of individuals. For crossover of object trees can be used following methods: crossover the parts of object trees crossover by linking trees or sub-trees The method of crossover object trees is based on the selection of two parents from the population and changing each other part of their sub-trees. For each of the parents cross points are randomly selected and their nodes and sub-trees are exchanged. This is the principle of creating new individuals into subsequent population as is shown on Fig. 1. Crossover the parts of object trees (sub-trees) Node of crossing Parrents – – num Node of crossing × + num Uk Uk U- DEk num Offsprings – Crossed nodes U- num × Crossed nodes – + num Uk DEk num Uk Fig. 1 Classical Crossover (CC) This method, as well as the previous one, is based on the crossover of two parents who are selected from the previous population. But the difference is in the way how the object trees are crossed. This method, unlike the previous one, does not exchange two randomly selected parts of the parents but parts of individuals are linked together with new and randomly generated node. This node will represent a new root of the tree structure of the individual. This principle is shown on Fig. 2. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 104 Node of crossing Parrents – – num Uk – DEk num Randomly generated node / U- – U- num Uk U- Offsprings – num + num Uk Randomly generated node Node of crossing × num num Uk Fig. 1. Crossover by linking method (LC Linking Crossing) Fig. 2 Crossover by linking method D Mutation Mutation is the second of the operators to obtain new individuals. This operator can add new structures, which are not included in the population so far. Mutation is performed on individuals from the old population. In the selected individual are randomly chosen nodes which are then subjected to mutation. The mutation operator can be subdivided into two types: Non-structural Mutation (NM) Structural Mutation (SM) Non-structural Mutation (NM) Non-structural mutations do not affect the structure of already generated individual. In the individual who is selected for mutation, chosen nodes of object sub-tree are further subjected to mutation. The mutation will randomly change chosen nodes, whereas used grammar is respected. For example it means that mutated node, which is a function of two variables (i.e. + - × ÷) cannot be changed by node representing function of one variable or only a variable, etc. (see Fig. 3). Node for mutation – × Ek-1 – + num Uk Mutated node Non structural mutation Ek-1 num Uk Fig. 3 Nonstructural mutation Structural Mutation (SM) Structural mutations, unlike non-structural mutations, affect the tree structure of individuals. Changes of the subtree by extending or shortening its parts depend on the method of structural mutations. Structural mutation can be divided into two types: Structural mutation which is extending an object tree structure (ESM) and structural mutation which is shortening a tree structure (SSM). This type of mutation operator can be subdivided into two types: ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 105 Structural mutation – Ek-1 – – num Uk-1 num Ek Shortening Extending Fig. 4 Structural mutation Extending Structural Mutation (ESM) In the case of the extending mutation, a randomly selected node is replaced by a part of the newly created subtree that respects the rules of defined grammar (see Fig. 3). This method obviously does not always lead to the extension of the sub-tree but generally this form of the mutation leads to extension of sub-tree. (see Fig. 4). In view of the object tree complexity of the individual and also for subsequent crossover is preferable to have a function in the form x = 3a than x = a + a + a, or more generally x = n × A. Another example is the shortening of the function x = ─ (─ a), where is preferable to have the form x = a (it is removing redundant marks in the object tree individual). The introduction of algebraic modifications of individual phenotype leads to the shorter result of the optimal solution and consequently to the shorter presentation of the individual, shortening the time of calculation of the function that is represented in object tree and also to find optimal solutions faster because of higher probability of crossover in the suitable points with higher probability to produce meaningful solutions. The essential difference stems from the use of direct contraction of trees, which leads to significantly shorter resulting structure than without using this method. E Hierarchical structure of TE for optimisation of the controller The hierarchical structure of the transplant evolution can be used for optimisation of the structure and parameters of a general controller. This structure contains three layers. First two layers (GE + DE) are contained in TE. Those two layers are used for optimisation of the structure and parameters of general controller. The third layer which is named layer of controller is used for computation of fitness in TE. At the beginning of TE an initial population is created and then fitness of individuals is calculated. In the case of finding the optimal solution in the first generation, the algorithm is terminated, otherwise creates a new population of individuals by crossover and mutation operators, with the direct use of already created parent’s object tree structures (it is analogy as transplantation of already created organs, without necessary know-ledge of DNA – “Transplant Evolution (TE)”). If the result of TE needs some numerical parameters (for example num in [10], the second level with Differential Evolution (DE) is used for optimization their parameter setting. The DE gives better results in finding optimal values of unknown numerical parameters that are expressed in the form of real numbers, then in the GE. Due to the use of TE for optimization of controllers in the next stage of calculation of fitness is model of controller used which is represented by the equation in incremental form (recurrent algorithm). Quality of controller is determined depending on the type of object function (3). For fitness calculation are various object functions used. Basic criterion is linear control area, quadratic control area, linear or quadratic control area extended with overshoot, oscillation of action value of the controller. We used are two types of fitness evaluation. First is used at the beginning for creation of computer network structure and second for optimization of parameters this structure. 4. CONCLUSION The Two-Level Transplant Evolution (TLTE) was successfully use for automatic generation of optimal computer network structure with the high through put. We tested this algorithm on many networks. We hope that this new method of network design will be use in practice, not only for simulation. The transplant evolution can be used with clustering to optimize the throughput of computer network We are far from supposing that all difficulties are removed but first results with TEs are very promising. We have prepared and tested optimization tools for increasing quality of computer networks ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 106 REFERENCES [1] KOZA, J. R. 1992: Genetic Programming: On the Programming of Computers by Means of Natural Selection, The MIT Press [2] KRATOCHVÍL, O.; OŠMERA, P.; POPELKA, O. 2009: Parallel grammatical evolution for circuit optimization, in Proc. WCECS, World Congress on Engineering and Computer Science, San Francisco, 1032-1040. [3] LI, Z.; HALANG, W. A.; CHEN, G. 2006: Integration of Fuzzy Logic and Chaos Theory; paragraph: Osmera P.: Evolution of Complexity, Springer, pp. 527 – 578. [4] O’NEILL, M.; RYAN, C. 2003: Grammatical Evolution: Evolutionary Automatic Programming in an Arbitrary Language Kluwer Academic Publishers. [5] O’NEILL, M.; BRABAZON, A.; ADLEY, C. 2004: The Automatic Generation of Programs for Classification Problems with Grammatical Swarm, Proceedings of CEC, Portland, Oregon, pp. 104 – 110. [6] PIASECZNY, W.; SUZUKI, H.; SAWAI, H. 2004: Chemical Genetic Programming – Evolution of Amino Acid Rewriting Rules Used for Genotype-Phenotype Translation, Proceedings of CEC, Portland, Oregon, pp. 1639 - 1646. [7] PRICE, K. 1996. Differential evolution: a fast and simple numerical optimizer, Biennial Conference of the North American Fuzzy Information Processing Society, NAFIPS, IEEE Press, New York, NY, pp. 524-527. [8] RUKOVANSKÝ, I. Optimization of the throughput of Computer Network Based on Parallel EA. In Proceedings of the World Congress on Engineering and Computer Science WCECS 2009, San Francisco, CA, Oct. 20-22, 2009, Vol. II, pp. 1038-1043 [9] WEISSER, R.; OŠMERA, P.; MATOUŠEK, R. Transplant Evolution with Modified Schema of Differential Evolution: Optimization Structure of Controllers. In International Conference on Soft Computing MENDEL. Brno : MENDEL, 2010, pp.113 - 120 [10] WEISSER, R.; OŠMERA, P.; ŠEDA, M.; KRATOCHVÍL, O. Transplant Evolution for Optimization of General Controllers. In European Conference on Modelling and Simulation. 24th. Kuala Lumpur (Malaysia) : ECMS 2010, pp. 250 -- 260. ADRESS: Prof. Ing. Imrich Rukovanský, CSc. Evropský polytechnický institute, s.r.o. Osvobození 699 686 04 Kunovice [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 107 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 108 MINISATION OF COMPLEXLOGICAL FUNCTIONS Miloš Šeda European Polytechnical Institute, Ltd. Kunovice Abstract: Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the well-known Quine-McCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the QuineMcCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the QuineMcCluskey method and show that it represents a set covering problem that, unfortunately, is an NPhard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings. Keywords: Boolean algebra, Karnaugh map, Quine-McCluskey method, set covering problem, genetic algorithm. 1. INTRODUCTION For minimisation of logical functions, laws of the Boolean algebra and the Karnaugh maps are mostly used. The Karnaugh maps represent a very efficient graphical tool for minimising logical functions with no more than 6 variables. However, their use is based on visual recognition of adjacent cells and, therefore, the method is not suitable for automated processing on computers. A direct application of the Boolean algebra laws is not restricted in this way, but there is no general algorithm defining the sequence of their application and thus this approach is not suitable for computer implementation either. With the growing strength of computational techniques, further investigations were focused on an algorithmbased technique for simplifying Boolean logic functions that could be used to handle a large number of variables. The well-known method usable on computers is the algorithm proposed by Edward J. McCluskey, professor of electrical engineering at University of Standford, and philosopher Willard van Orman Quine from Harvard University [13], [18]. We will assume that the number of variables n may be high but restricted in the sense that all 2n rows of the corresponding truth table may be saved in a memory and thus may be processed. If this condition is not satisfied, then we could only work with a selected number of truth table rows. This approach is possible, e.g., in image filters [19]. Of course, this is inacceptable in real logic control applications where all input combinations must be tested. In the next considerations we will assume the full truth table. 2. QUINE-MCCLUSKEY METHOD The Quine-McCluskey method [13], [17], [18] is an exact algorithm based on systematic application of the distributive law (1), complement law (2) and idempotence law (3), i.e. the laws as follows: x.( y z ) xy xz (1) x x 1 (2) x x x (3) From (1) and (2), we can easily derive the uniting theorem (4) xy x y x.( y y) x.1 x (4) ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 109 In general, this means that two expressions with the same set of variables differing only in one variable with complementary occurrence may be reduced to one expression given by their common part, e.g. f xyzw xyzw xzw( x x) xzw.1 xzw For next considerations we will need the following notions: Literal is a variable or its negation. Term is a conjunction (= product) of literals. Minterm is a conjunction of literals including every variable of the function exactly once in true or complemented form. For example, if , then and are terms and minterms are represented by conjunctions and because . Disjunctive normal form (DNF) of a formula f is a formula f’ such that f’ is equivalent to f and f’ has the form of a disjunction of conjunctions of literals. Canonical (or complete) disjunctive normal form (CDNF) is a DNF where all conjunctions are represented by minterms. Now we can describe a skeleton of the Quine-McCluskey method: 1. Minterms of a given Boolean function in CDNF are divided into groups such that minterms with the same number of negations are in the same group. 2. All pairs of terms from adjacent groups (i.e. groups whose number of negations differ by one) are compared. 3. If compared terms differ only in one literal (and the uniting theorem may be applied) then these terms are removed and a term reduced to a common part is carried to the next iteration. 4. All terms are used only once, i.e. if necessary the idempotence law is applied. 5. If the number of terms in the new iteration is nonzero, then steps 2-5 are repeated, otherwise the algorithm finishes. The result of the algorithm is represented by the terms that were not removed, i.e. that could not be simplified. Now, we will apply the Quine-McCluskey method to a simple logical function from [5] and, by means of the Karnaugh map, we will show that it will not find its minimal form. Example 1 Minimise the following logical function in CDNF. f x yzw x y zw xyz w x yz w x y z w xyz w x y zw x y z w x y zw Solution: If we divide the minterms into groups by the number of their negations, then we get this initial iteration: (0) xyzw ; x yzw ; xyzw ; xyzw ; x y zw ; xyz w ; x y zw ; x y z w ; x y zw If we compare all pairs of terms from adjacent groups in the initial iteration (0) and place in frames terms that can be simplified and divide the resulting terms in the next iteration (1) into groups again, then we get: (0) xyzw ; x yzw ; xyzw ; xyzw ; x y zw ; xyz w ; x y zw ; x y z w ; x y zw (1) x yz ; x zw ; x y z ; y zw ; x y w ; xyz ; xz w ; xzw ; y zw ; x y z ; ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 110 Applying the previous steps to iteration (1), we get: (1) xyz ; xzw ; x y z ; y zw ; x yw ; xyz ; xzw ; xzw ; y zw ; x y z ; (2) xz ; y z In iteration (2) we have only one group of terms and thus no simplified terms can be generated and the algorithm finishes. Its result fm is given by a disjunction of those terms that cannot be simplified. f m xz y z x yw xyz xzw Let us consider the same example and solve it using the Karnaugh map. For the given Boolean function f, we get the following map x w 1 1 1 1 1 1 1 1 1 y z Fig. 1 Karnaugh map From this map, we get two possible solutions of a minimal logical function depending on the way of covering the first two cells with logical 1 in the last columns. a) f1min xz yz xyw xyz b) f 2 min xz yz xzw xyz We can see that the result gained using Karnaugh map includes a lower number of terms than the result of computation by means of Quine-McCluskey method. S. R. Petrick proposed a modification of Quine-McCluskey method that tries to remove the resulting redundancy [16]. The Quine-McCluskey simplification technique with special modifications is presented in [21]. Before describing the second phase of computation, we will define several notions. (i) A Boolean term g is an implicant of a Boolean term f if: each literal in g is also obtained in f (i.e. if g has the form g(x1, ... , xn) then f has the form f(x1, ... , xn, y1, … , ym)), and for all combinations of literals the implication g f has a value of True. We know that the implication is defined by Table 1. From this definition, we get that g is an implicant of f if and only if g f. In our case, that means that the second property is satisfied if g(x1, ... , xn) f(x1, ... , xn, y1, … , ym) for each selection of x1, ... , xn and each selection of y1, … , ym. g 0 0 1 1 TABLE 1 IMPLICATION f 0 1 0 1 g f 1 1 0 1 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 111 Therefore, we can consider only those values of variables at which g is true and, for all these cases, f must also be true. (ii) The terms resulting from the Quine-McCluskey method are called prime implicants. In the Petrick modification of the Quine-McCluskey method, a table of prime implicants given by the results of the first phase is built. It has prime implicants in the heads of columns, minterms from a given CNDF are in the heads of rows and, in cells representing intersection the prime implicant in question is a subset of a corresponding minterm. We say that prime implicants cover minterms. In our example then we get Table 2 as follows. Although the prime implicants cannot be simplified, some of them can be redundant and thus may be omitted. disjunction of prime implicants would not express the initial canonical (complete) disjunctive normal form, i.e., there would be a non-covered minterm. omitted. Such implicants are called essential prime implicants. In our example there are three essential prime implicants: , and . symbols. We get Table 3. TABLE 2 COVERING OF MINTERMS BY PRIME IMPLICANTS xz xyzw yz xy w xyzw xyz w xy zw x y zw x y zw x y zw xz w x y zw xyzw xy z TABLE 3 xy zw xy w xz w It can be easily seen that, in simplified Table 3, the minterm x y z w may be covered by the prime implicant x y w or by xzw . Hence we get two minimal disjunctive forms: f1min xz yz xyw xyz and f 2 min xz yz xzw xyz , which agrees with the previous solution by the Karnaugh map. Although computations by the Quine-McCluskey method with the Petrick modification have a wider use than the approach based on the Karnaugh map, however, this improved method has also its restrictions. The main problem is in the procedure of covering minterms by prime implicants. It can be easily found if the number of ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 112 the essential prime implicants is high and thus the table of prime implicants will be very reduced. In general, we cannot expect this, and it is even possible that none of the prime implicants is essential. From the combinatorial optimisation theory, it is known that the set covering problem is NP-hard and its time complexity grows exponentially with the growing input size. It can be shown that, for a CNDF with n minterms, the upper bound of the number of prime implicants is 3n/n. If n=32, we can get more than 6.5 * 1015 prime implicants. To solve such a large instance of the set covering problem is only possible by heuristics (stochastic or deterministic) [1], [2], [4], [6], [10], [11], [14], [15], [20], [22] or by approximation [7], [8] methods. However, they do not guarantee an optimal solution. A formal definition of the problem and possible solution by a genetic algorithm is proposed in the next section. 3. SET COVERING PROBLEM (SCP) The set covering problem (SCP) is the problem of covering the rows of a m-row, n-column, zero-one matrix (aij) by a subset of columns at a minimal cost. Defining xj1 if column j (with cost cj0) is in the solution and xj0 otherwise, the SCP is: n Minimise cjxj (5) j 1 subject to n aij x j 1, i 1, 2,..., m, (6) j 1 x j {0,1}, j 1, 2,..., n (7) Constraints (6) ensure that each row is covered by at least one column and (7) is a constraint guaranteeing integers. In general, the cost coefficients cj are positive integers. Here, in the application of the SCP for the second phase of the Quine-McCluskey method, we assume all cj equal to 1 because we try to minimise the number of the covering columns. This special case of SCP is called a unicost SCP. SCP has, besides Quine-McCluskey method, a wide range of applications, for example vehicle and crew scheduling [12], facilities location [1], assembly line balancing and Boolean expression simplification. There are number of other combinatorial problems that can be formulated as, or transformed to, SCP such as the graph colouring problem [1] and the independent vertex set problem [7]. A fuzzy version of SCP is studied in [3] and [9]. Since we use, for solving the SCP, a modified version of the genetic algorithm (GA) proposed by Beasley and Chu [2], [4] for the non-unicost SCP, we summarise the basic properties of GAs. 4. GENETIC ALGORITHM The skeleton for GA can be described as follows: generate an initial population ; evaluate fitness of individuals in the population ; repeat select parents from the population; recombine (mate) parents to produce children ; evaluate fitness of the children ; replace some or all of the population by the children until a satisfactory solution has been found ; Since the principles of GAs are well-known, we will only deal with GA parameter settings for the problems to be studied. Now we describe the general settings. Individuals in the population (chromosomes) are represented as binary strings of length n, where a value of 0 or ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 113 1 at the i-th bit (gene) implies that xi = 0 or 1 in the solution respectively. The population size N is usually set between n and 2n. Many empirical results have shown that population sizes in the range [50, 200] work quite well for most problems. Initial population is obtained by generating random strings of 0s and 1s in the following way: First, all bits in all strings are set to 0, and then, for each of the strings, randomly selected bits are set to 1 until the solutions (represented by strings) are feasible. The fitness function corresponds to the objective function to be maximised or minimised. There are three most commonly used methods of selection of two parent solution for reproduction: proportionate selection, ranking selection, and tournament selection. The tournament selection is perhaps the simplest and most efficient among these three methods. We use the binary tournament selection method where two individuals are chosen randomly from the population. The more fit individual is then allocated a reproductive trial. In order to produce a child, two binary tournaments are held, each of which produces one parent. The recombination is provided by the uniform crossover operator, which has a better recombination potential than do other crossover operators as the classical one-point and two-point crossover operators. The uniform crossover operator works by generating a random crossover mask B (using Bernoulli distribution) which can be represented as a binary string B = b1b2b3 ··· bn-1bn where n is the length of the chromosome. Let P1 and P2 be the parent strings P1[1], ... ,P1[n] and P2[1], ... ,P2[n] respectively. Then the child solution is created by letting: C[i] = P1[i] if bi = 0 and C[i] = P2[i] if bi = 1. Mutation is applied to each child after crossover. It works by inverting M randomly chosen bits in a string where M is experimentally determined. We use a mutation rate of 5/n as a lower bound on the optimal mutation rate. It is equivalent to mutating five randomly chosen bits per string. When v child solutions have been generated, the children will replace v members of the existing population to keep the population size constant, and the reproductive cycle will restart. As the replacement of the whole parent population does not guarantee that the best member of a population will survive into the next generation, it is better to use steady-state or incremental replacement which generates and replaces only a few members (typically 1 or 2) of the population during each generation. The least-fit member, or a randomly selected member with below-average fitness, are usually chosen for replacement. Termination of a GA is usually controlled by specifying a maximum number of generations tmax or relative improvement of the best objective function value over generations. Since the optimal solution values for most problems are not known, we choose tmax 5000. 5. GENETIC ALGORITHM FOR SCP The chromosome is represented by an n-bit binary string S where n is the number of columns in the SCP. A value of 1 for the j-th bit implies that column j is in the solution and 0 otherwise. Since the SCP is a minimisation problem, the lower the fitness value, the more fit the solution is. The fitness of a chromosome for the unicost SCP is calculated by (8). n f ( S ) S[ j ] (8) j 1 The binary representation causes problems with generating infeasible chromosomes, e.g. in initial population, in crossover and/or mutation operations. To avoid infeasible solutions a repair operator is applied. Let I = {1, … , m} = the set of all rows; J = {1, … , n} = the set of all columns; i = {jJ | aij 1} = the set of columns that cover row i, iI; j = {iI | aij 1} = the set of rows covered by column j, jJ; S = the set of columns in a solution; U = the set of uncovered rows; wi = the number of columns that cover row i, iI in S. The repair operator for the unicost SCP has the following form: ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 114 initialise wi : = | S i | , i I ; initialise U : = { i | wi = 0 , i I } ; for each row i in U (in increasing order of i) do begin find the first column j (in increasing order of j) in i that minimises 1/ |U j | ; S:=S+j; wi : = wi + 1, i j ; U:=Uj end ; for each column j in S (in decreasing order of j) do if wi 2 , i j then begin S : = S j ; wi : = wi 1, i j end ; { S is now a feasible solution to the SCP and contains no redundant columns } Initialising steps identify the uncovered rows. For statements are “greedy” heuristics in the sense that in the 1 st for, columns with low cost-ratios are being considered first and in the 2nd for, columns with high costs are dropped first whenever possible. 6. CONCLUSION In this paper, we studied the problem of minimising the Boolean functions with a rather high number of variables. Since traditional approaches based on the Boolean algebra or Karnaugh maps have restrictions in the number of variables and the sequence of laws that could be applied is not unique, we focus on the well-known Quine-McCluskey method. Since it does not guarantee the finding of an optimal solution, we must apply a postprocessing phase. Unfortunately, the data resulting from the Quine-McCluskey method are in the form of a unicost set covering problem, which is NP-hard. Therefore, for logical functions, the obvious Petrick’s extension of the Quine-McCluskey method cannot be applied, and heuristic or approximation method must be used instead. We proposed a genetic algorithm-based approach and discussed problem-oriented parameter settings. In the future, we are going to implement also other stochastic heuristics, such as simulated annealing and tabusearch, and compare them with the genetic algorithm. REFERENCES [1] BROTCORNE, L.; LAPORTE, G.; SEMET, F. Fast Heuristics for Large Scale Covering-Location Problems. Computers & Operations Research, vol. 29, pp. 651-665, 2002. [2] BEASLEY, J. E.; CHU, P. C. A Genetic Algorithm for the Set Covering Problem. Journal of Operational Research, vol. 95, no. 2, pp. 393-404, 1996. [3] CHIANG, C. I.; HWANG, M. J.; LIU, Y. H. An Alternative Formulation for Certain Fuzzy SetCovering Problems. Mathematical and Computer Modelling, vol. 42, pp. 363-365, 2005. [4] CHU, P. A Genetic Algorithm Approach for Combinatorial Optimisation Problems. PhD thesis, The Management School Imperial College of Science, Technology and Medicine, London, 1997. [5] ČULÍK, K.; SKALICKÁ, M.; VÁŇOVÁ, I. Logic (in Czech). Brno: VUT FE, 1968. [6] GALINIER, P.; HERTZ, A. Solution Techniques for the Large Set Covering Problem. Discrete Applied Mathematics, vol. 155, pp. 312-326, 2007. [7] GOMES, F. C.; MENESES, C. N.; PARDALOS, P. M.; VIANA, G. V. R. Experimental Analysis of Approximation Algorithms for the Vertex Cover and Set Covering Problems. Computers & Operations Research, vol. 33, pp. 3520-3534, 2006. [8] GROSSMAN, T.; WOOL, A. Computational Experience with Approximation Algorithms for the Set Covering Problem. European Journal of Operational Research, vol. 101, pp. 81-92, 1997. [9] HWANG, M. J.; CHIANG, C. I.; LIU, Y. H. Solving a Fuzzy Set-Covering Problem. Mathematical and Computer Modelling, vol. 40, pp. 861-865, 2004. [10] LAN, G.; DEPUY, G. W. On the Effectiveness of Incorporating Randomness and Memory into a MultiStart Metaheuristic with Application to the Set Covering Problem. Computers & Industrial Engineering, vol. 51, pp. 362-374, 2006. [11] LAN, G.; DEPUY, G. W.; WHITEHOUSE, G. E. 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ADRESS: Prof. RNDr. Miloš Šeda, Ph.D. European Polytechnical Institute, Ltd. Osvobození 699, 686 04 Kunovice, Czech Republic e-mail: [email protected], [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 116 PERFORMANCE MODELLING OF MULTIPROCESSOR PARALLEL SYSTEMS Dan Slovaček European polytechnic institute, Kunovice Abstract: The using of parallel principles is the most effective way how to increase the performance of applications (parallel computers and algorithms). In this sense the paper is devoted to performance modelling of parallel computers. Therefore the paper describes the typical parallel computers and then he summarised the basic concepts performance modelling of them. Current trends in high performance computing (HPC) and grid computing (Grid) are to use networks of workstations (NOW) as a cheaper alternative to traditionally used massively parallel multiprocessors or supercomputers. There has been an increasing interest in the use of networks of workstations connected together by high speed networks (Fig.2) for solving large computation intensive problems. This trend is mainly driven by the cost effectiveness of such systems as compared to massive multiprocessor systems with tightly coupled processors and memories (Supercomputers). Parallel computing on a cluster of workstations connected by high speed networks has given rise to a range of hardware and network related issues on any given platform. Keywords: parallel computer, virtual parallel system, network of workstations, performance modelling 1. INTRODUCTION Principal example of networks of workstations also for solving large computation intensive problems is at Fig. 1. The individual workstations are mainly extreme powerful personal workstations based on multiprocessor or multicore platform. Parallel computing on a cluster of workstations connected by high speed networks has given rise to a range of hardware and network related issues on any given platform. PC 1 PC 2 PC 3 ... PC n - Myrinet switch - Myrinet ports - 1G Ethernet (10G Ethernet) ports Fig.1. Architecture of NOW (Myrinet, Ethernet, Infiniband etc.). With the availability of cheap personal computers, workstations and networking devises, the recent trend is to connect a number of such workstations to solve computation intensive tasks in parallel on various integrated forms of NOW. Fig. 2 illustrates typical complex integrated module of NOW networks. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 117 GRID Modul (SMP, NOW) Laboratory 1 1 Switch 1 i 1 2 Laboratory 2 1 Switch 2 i Switch n (central) . . . Laboratory n -1 1 Switch n -1 i Router i Fig.2. Integration of NOW networks. 2. THE ROLE OF PERFORMANCE Quantitative evaluation and modelling of hardware and software components of parallel systems are critical for the delivery of high performance. Performance studies apply to initial design phases as well as to procurement, tuning and capacity planning analysis. As performance cannot be expressed by quantities independent of the system workload, the quantitative characterisation of resource demands of application and of their behaviour is an important part of any performance evaluation study [1, 2, 3]. Among the goals of parallel systems performance analysis are to assess the performance of a system or a system component or an application, to investigate the match between requirements and system architecture characteristics, to identify the features that have a significant impact on the application execution time, to predict the performance of a particular application on a given parallel system, to evaluate different structures of parallel applications. In order to extend the applicability of analytical techniques to the parallel processing domain, various enhancements have been introduced to model phenomena such as simultaneous resource possession, fork and join mechanism, blocking and synchronisation. Modelling techniques allow to model contention both at hardware and software levels by combining approximate solutions and analytical methods. However, the complexity of parallel systems and algorithms limit the applicability of these techniques. Therefore, in spite of its computation and time requirements, simulation is extensively used as it imposes no constraints on modelling. Evaluating system performance via experimental measurements is a very useful alternative for parallel systems and algorithms. Measurements can be gathered on existing systems by means of benchmark applications that aim at stressing specific aspects of the parallel systems and algorithms. Even though benchmarks can be used in all types of performance studies, their main field of application is competitive procurement and performance assessment of existing systems and algorithms. Parallel benchmarks extend the traditional sequential ones by providing a wider a wider set of suites that exercise each system component targeted workload. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 118 3. PERFORMANCE MODELLING To evaluating parallel algorithms there have been developed several fundamental concepts. Tradeoffs among these performance factors are often encountered in real-life applications. To the performance evaluation we can use following methods analytical methods application of queuing theory results [1 4, 14] asymptotic analyses [7, 8, 9] simulation methods [12] benchmarks [5, 10, 13] direct measuring (parallel computers and algorithms) [6, 12]. Evaluating system performance via experimental measurements is a very useful alternative for parallel systems and algorithms. Measurements can be gathered on existing systems by means of benchmark applications that aim at stressing specific aspects of the parallel systems and algorithms. Even though benchmarks can be used in all types of performance studies, their main field of application is competitive procurement and performance assessment of existing systems and algorithms. Parallel benchmarks extend the traditional sequential ones by providing a wider a wider set of suites that exercise each system component targeted workload. 3.1. THE ANALYTICAL APPROACH For the mathematical model of the computer networks it is necessary to specify statistical character of the input demand stream (the input stream of data unities, number and length of data unities etc.) servicing network (the servicing nodes, topology of servicing network, number of servicing devices, servicing types, servicing character etc.) servicing times a way of servicing (FIFO – First In First Out, LIFO – Last In First Out, servicing with priorities) limited or unlimited number of buffers for sorting the transmitted data unities and the algorithms of their assigning. To the most existed mathematical models we do not know their exact analytical solution. The main causes which complicate of analytical solution are the specific distribution of real data flows the complicated servicing structures the mutual dependencies of the wanted values and control data flows the complications in the control activities of the real system (priorities, physical limitations of the used system components as for example of the used system components as for example waiting queues, interrupted activities of the devices etc.). For the analytical solutions they are from the point of solution complexity the most suitable the models with exponential random distribution (for example the inter arrival input times or servicing time etc.) In the cases in which we are not able to approximate the real variables with no defined random distributions the analytical solution is unable even in the simplest cases. 3.2 THE SIMULATION METHOD This method is based on the simulation of the basic characteristics that are the input data stream and their servicing according the measured and analyzed probability values simulate the behaviour model of the analyzed system. Its part is therefore the time registration of the wanted interested discrete values. The result values of simulation model have always their discrete character (discrete numerous values), which do not have the universal form of mathematical formulas to which we can set when we need the variables of the used distributions as in the case of analytical models. The accuracy of simulation model depends therefore on the accuracy measure of the used simulation model for the given task. It is very important to find the suitable dividing line of the application using of both methods. For the application area of the distributed computer system it is very effective their mutual interlace and complementation. For example for the behaviour analyze of the independent queuing theory system is in principal simpler to use the derived analytical results. In case of serially connected queuing theory systems the outgoing method is the ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 119 simulation because the application of the analytical methods is very problematic. In common the using of simulation method is mainly in following cases models have large number of variables and function, which are changing in time intervals variables are influenced through various disturbing influences of random character with various distributions and with many mutual structures models are mutual connected with particular models of various operations and the possibility of outstanding intervention existence of limitations in trajectories of model variables an limits in model combinations no existence of any suitable analytical method and therefore the using of simulation method is the only analyzing tool. Even if the discrete simulation can contribute to the behaviour analyze of the distributed computer network for the analysis of the large complex computer networks is very unpractical and unusable. His disadvantage is also that the achieved results are not universal. But it is very useful in these cases in which we are not able apply any analytical method and so the simulation methods is the only analytical tool or in cases in which exist only approximate analytical methods and the simulation became the verification tool of achieved analytical results. 4. PERFORMANCE CRITERIONS 4.1. PERFORMANCE TESTS Classical Peak performance Dhrystone Whetstone LINPAC Khornestone Problem oriented tests (Benchmarks) SPEC tests 4.2. SPEC TESTS 4.2.1. SPEC RATIO SPEC (Standard performance evaluation corporation - www.spec.org) defined one number to summarise all needed tests for integer number. Execution times are at first normalised through dividing execution time by value of reference processor (chosen by SPEC) with execution time on measured computer (user application program). The achieved ratio is labelled as SPEC ratio, which has such advantage that higher numerical numbers represent higher performance, that means that SPEC ratio is an inversion of execution time. INT 20xx (xx means year of latest version) or CFP 20xx result value is produced as geometric average value of all SPEC ratios. The relation for geometric average value is given as n n normalised execution time i 1 i , where normalised execution time is the execution time normalised by reference computer for i – th tested program from whole tested group n (all tests) and n a i 1 i product of individual ai . ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 120 4.2.2. SPEC INT RESULTS SPEC INT results for AMD Operon X4 model are in Tab.1. 1. Description Name Instr. count CPI [10 9] String processing Perl 2 188 0,75 Clock cycle time [ns] 0,4 637 9 770 15,3 Block-sorting compression GNU C compiler Combinatorial optimisation Go game bzip2 2 389 0,85 0,4 817 9 650 11,8 Gcc 1 050 1,72 0,4 724 8 050 11,14 mcf 336 10,00 0,4 1 345 9 120 6,8 go 1 658 1,09 0,4 721 10 490 14,6 Search gene hmmer sequence Chess game (AI) sjeng 2 783 0,80 0,4 890 9 330 10,5 2 176 0,96 0,4 837 12 100 14,5 Quantum Libquantum computer simulation Video h264avc compression Discrete event omnetpp simulation library Games/path astar finding XML parsing xalancbmk 1 623 1,61 0,4 1 047 20 720 19,8 3 102 0,80 0,4 993 22 130 22,3 587 2,94 0,4 690 6 250 9,1 1 082 1,79 0,4 773 7 020 9,1 1 058 2,70 0,4 1 143 6 900 Geometric mean Execution time [s] Reference time [s] SPEC ratio 6,0 11,7 Tab.1.1. SPEC INT results for AMD Opteron X4 model 2356. 5. REAL MODELS Generally model is the abstraction of the system. The functionality of the model represents the level of the abstraction applied. That means, if we know all there is about the system and are willing to pay for the complexity of building a true model, the role of abstraction is near nil. In practical cases we wish to abstract the view we take of a system to simplify the complexity of the real system. We wish to build a model that focuses on some basic elements of our interest and leave the rest of real system as only an interface with no details beyond proper inputs and outputs. Real system is a real process or system that we wish to model. In our case it is the process of performance of parallel algorithms (PA) for used parallel computers (SMP, NOW, GRID). The basic conclusion is that a model is a subjective view of modeller’s subjective insight into modelled real system. This personal view defines what is important, what the purposes are, details, boundaries, and so one. Therefore the modeller must understand the system in order to guarantee useful features of the created model. 6. CONCLUSIONS In our home conditions we have been intensively dealing with virtual parallel systems based on network of personal computers (SMP, NOW) for many years and in later four years also with more complex Grid system. Based on mentioned virtual parallel architectures we developed real models according Fig.3. to analyse their complexity and performance. We will referee to them in next articles. Now according current trends in virtual parallel computers (SMP, NOW, Grid), based of powerful personal computers and also Internet computing (Cloud computing), we are looking for a flexible model of virtual parallel computer that supports both parallel and distributed computers. In such unified model we would like to study load balancing, inter-process communication (IPC), transport protocols, performance prediction etc. We would refer to results later in scientific journals. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 121 Fig. 3. Real performance modelling. The intent of this paper is to evolve the important role of performance modelling for actual parallel computer (NOW, Grid) for solving complex problems, which are widely present also in other scientific areas than only in to this time mainly analysed complex problems from application informatics. REFERENCES [1] GELENBE, E. Computer system performance modeling in perspective, 288 pages, published September 2006, Imperial College Press. [2] HANULIAK, I.; HANULIAK, P. Performance evaluation of iterative parallel algorithms, United Kingdom : Kybernetes, Volume 39, No.1, 2010, pp. 107- 126. [3] HANULIAK, I.; HANULIAK, P. To performance modelling of parallel algorithms, ICSC 2011, Kunovice : sekcia č. 2, pp 125 - 132, Czech republic [4] HANULIAK, P. Parallel iteration algorithms for Laplacean equation method, ICSC 2012, Kunovice : Czech republic (in print). [5] HANULIAK, P.; SLOVÁČEK, D. To performance modeling of virtual computers, In Proc.: TRANSCOM 2011 - section 3, Žilina : pp. 213 – 216, 2011. [6] HUDIK, M. Performance optimization of broadcast collective operation on multi-core cluster, ICSC Leden 2012, Kunovice : Czech republic (in print). [7] HUDIK, M.; HANULIAK, P. Analysing Performance of Parallel Algorithms for Linear System Equations, In Proc.: GCCP 2011, October 24-26, Bratislava : pp. 70-77, 2011, SAV Institute of Informatics. [8] HUDIK, M.; HANULIAK, P. Parallel complexity of linear system equation, In Proc.: TRANSCOM 2011 - section 3, Žilina : pp. 107-110, 2011. [9] JANOVIČ, F. Modelovanie výkonnosti distribuovaných paralelných algoritmov, ICSC Leden 2012, Kunovice : Czech republic (in print) [10] KIRK, D. B.; HWU, W. W. Programming massively parallel processors, Morgam Kaufmann, 280 pages, 2010 [11] KUMAR, A.; MANJUNATH, D.; KURI, J. Communication Networking , 750 pp., 2004, Morgan Kaufmann [12] LILJA, D. J.; Measuring Computer Performance, United Kingdom : 2005, University of Minnesota, Cambridge University Press. 280 p. [13] PATERSON, D. A.; HENNESSY, J. L. Computer Organisation and Design, 912 pp., Morgan Kaufmann, 2009. [14] SLOVÁČEK, D.; HANULIAK, P. Analysis of computer performance, In Proc. MMK 2010, Hradec Králové : pp. 42-51, 2010, 6.-10 Prosinec, Czech republic ADDRESS: Mgr. Dan Slovaček European Polytechnic Institute Osvobozeni 699 686 04, Kunovice [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 122 DESIGN AND CONSTRUCTION OF EXPERT SYSTEM FOR ANALYSIS OF RECREATION ATTRACTIVENESS Yaroslav Vyklyuk, Olga Artemenko Bucovinian University, Ukraine This paper describes designing and developing an expert system for analysis of territory recreational attractiveness. An analysis of recent researches was done to find an optimal combination of intelligent methods of modeling to meet the capabilities of geographic information systems to support decisions and forecasting in tourism. Keywords: fuzzy logic, expert system, recreation attractiveness. INTRODUCTION Tourism can be a major push factor for socio-economic development. After all, tourism is not only provides a large number of jobs in services, but also affects the development of such industries as transportation, construction, trade, communications and entertainment industry. In addition, tourism has a high profitability, and is less capital-intensive than other types of business activity [1]. Tourism includes many species and fields. The combination in time and space tourist related services, recreational resources, and infrastructure is a difficult task. Therefore, predicting the spatial location, operation and development of tourism and recreation systems using mathematical and intelligent methods of data analysis is one of the important directions of research. Among other things, information about promising for the creation and development of tourism infrastructure area, are interested not only investors but also state and local authorities. It can identify promising areas of recreation will find attractive for investment objects, as well as in scientific basis for the strategy of economic development of tourism in the regions. PURPOSE AND RESEARCH ACTUALITY A research purpose was to build a conceptual model of expert system analysis of recreational attractiveness of the area, allowing an analysis of attractiveness for tourism business and tourism and recreation systems in the region to the scientific study of their development strategy. Research actuality was to explore the possibilities of using information technology for solving the problem of assessment, optimization and forecasting in tourism. The practical value of the study: the structure of expert system is built and types and directions of information flows are defined. We also show how to implement such an expert system. DEVELOPMENT OF A CONCEPTUAL MODEL OF EXPERT SYSTEM Analysis of information technology used in the world to study and optimization of Tourism shows that most research focuses on modeling and optimization of existing tourist and recreation systems. The problem of modeling of the origin and dynamics of development of new tourism and recreation systems is not solved. The main objective is to choose the optimal location for building, structure prediction of tourist flows, the choice of optimal strategy performance, forecasting and management of spatial development of urban areas. So, based on analysis of collected data can be considered tasks that need to be addressed through the development and improvement of information technology for tourism are: calculation of attractiveness of the territory and spatial distribution of urbanization. The attractiveness of the area for tourists is determined by many factors, including qualitative and often ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 123 subjective. In order to analyze the attractiveness of large areas statistical information should be collected. Geographical characteristics of the territory can be obtained from databases of geographic information systems. Unlike the widely used classical methods of modeling attractiveness of the area, the apparatus of fuzzy logic not only allows you to work with parameters, in which there is linguistic ambiguity, but also greatly simplifies the process of getting a result [2]. A number of studies on tourism, also used fuzzy modeling. For example, the definition of tourist flows in the U.S. [3], a site selection expert system [4]. Determining the optimal location of international hotels have made on the basis of fuzzy logic in [5]. Building models that describe aspects of the functioning of the tourism industry and forecasting processes in her devoted work [6-8]. In addition, forecasting under uncertainty (eg, the demand for tourist services) can be implemented using fuzzy models [9]. Cellular automata are used to predict the development of urban infrastructure in the software iCity [10]. A research purpose was to create software that will allow the user to make informed and effective decisions on tourism businesses. Users are creating an expert system should become entrepreneurs, tourism industry experts and officials of regional governments and local authorities, whose job in some way connected with tourism. Analysis of the domain allowed a list of tasks that should solve the effective expert system analysis of the attractiveness of the area. Developed by the expert system should solve the problem: Decisions about the advisability of investing in tourism in the area; Making decisions for optimizing the list of travel services for some existing tourist and recreational facility (TRO); Evaluation of recreational resources and decision-making regarding the possibility of their use; Localization of areas with the most favorable conditions for building tourist facilities; Making decisions on the development of transport and social infrastructure to facilitate the development of tourist business. The external environment The simulation results Problems to be solved Statistical data User Expert Knowledge Spot territory attractiveness Decisions on investment 5 Territory parameters GIS Roads, water, slope height, forests, urbanization, geographic coordinates of objects Population Territory parameters The amount of services provided 3 DB Integral territory attractiveness Optimization of the list of tourist services Territiry 2 Rules Modeling of territory attractiveness 1 Convert geodata in the matrix of input parameters knowledge training Spatial distribution of recreational attractiveness Spot recreational potential Matrixes of attractiveness Estimation of recreational resources Determination of optimal areas for development Rules Modeling of recreational potential Territory Transport and accommodation infrastructure Integral recreational potential Decisions on development of transport and social infrastructure The existing infrastructure, limitation Expert system Forecast maps of the spatial distribution round. infrastructure 4 Modeling of the development of tourism infrastructure Terrytory, forcast time horizon Picture 1. The conceptual model of expert system CONCLUSIONS This paper describes the structure of an expert system for calculation and analysis of recreational attractiveness ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 124 of territory. This expert system enable to define perspective places for developing tourist infrastructure. The maps of spatial distribution of territory attractiveness, produced with our expert system, allow monitoring the change of territory’s attractiveness during a year. First of all, the offered method will allow the tourist industry investors to elect more effectively direction and dimensions of capital investments in planning their strategy, arranging PR-actions. Secondly, the regional government gets a scientific base which allows to make effective strategy for regional development and to optimize activity of tourist industry in the region. The offered system allows building the maps of recreation attractiveness for any territory. The used method for calculation the potential attractiveness of territory takes into account various parameters; therefore the received results give a complex representation of territory’s perspectives for tourist business. REFERENCES [1] YAKIN, V.; RUDENKO, V.; KOROLJ, O.; KRACHILO, M.; GOSTYUK, M.; OTHERS (2006). Problems of geography and tourism management. Chernivtsi: Chernivtsi national university. [2] LEONENKOV, A. (2005). Fuzzy modelling in MATLAB and fuzzyTECH. St. Petersburg.: БХВПетербург. [3] CATHY, H. C.; HSU, KARA WOLFE, SOO K. KANG. Image assessment for a destination with limited comparative advantages // Tourism Management, 2004. - #25., p.121–126 [4] NGAI, E. W. T.; WAT, F. K. T. Design and development ofa fuzzy expert system for hotel selection // Omega, 2003. - #31, p.275 – 286 [5] TSUNG-YU CHOU, MEI-CHYI CHEN, CHIA-LUN HSU. A fuzzy multi-criteria decision model for international tourist hotels location selection // International Journal of Hospitality Management 2007. [6] CHAO-HUNG WANG, LI-CHANG HSU. Constructing and applying an improved fuzzy time series model: Taking the tourism industry for example // Expert Systems with Applications, 2007. [7] WEN-BAO LIN An empirical of service quality model from the viewpoint of management // Expert Systems with Applications, 2007. - #32, p.364–375 [8] WEN-BAO LIN The exploration of customer satisfaction model from a comprehensive perspective // Expert Systems with Applications, 2007. - #33, p.110–121 [9] CHAO-HUNG WANG. Predicting tourism demand using fuzzy time series and hybrid grey theory // Tourism Management, 2004. - #25, p. 367–374 [10] STEVENS, D. iCity: A GISeCA modelling tool for urban planning and decision making / D. Stevens, S. Dragicevic, K. Rothley // Environmental Modelling & Software. – 2007 – №22 – p. 761-773. ADRESS: Yaroslav Vyklyuk Bucovinian University, Simovich str. 21, Chernictsi, 58000, Ukraine E-mail: [email protected] Olga Artemenko Bucovinian University, Simovich str. 21, Chernictsi, 58000, Ukraine E-mail: [email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 125 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 126 PRINCÍPY OPRIMALIZÁCIE NAVRHOVANIA ELEKTROMECHANICKÝCH AKČNÝCH ČLENOV Juraj Wagner Evropský polytechnický institut, s.r.o. Abstrakt: Príspevok sa zaoberá teoretickými základmi optimalizačných metód s dôrazom na uplatnenie metód statickej optimalizácie pri optimalizácii návrhu elektromechanických akčných členov mechatronických systémov s využitím počítačových metód navrhovania. Kľúčové slová: optimalizácia, optimalizačná metóda, mechatronické systémy, počítačové metódy navrhovania elektromechanické akčné členy, ÚVOD Pri návrhu každého elektromechanického akčného člena, jeho elektromagnetickom výpočte (návrhu elektrického a magnetického obvodu) a pri návrhu hlavných rozmerov, vychádzame zvyčajne zo zadania, ktoré definuje hlavné vstupné parametre (napájacie napätie, prúd, frekvencia, rozmery atď.) a hlavné výstupné parametre (výkon, moment, otáčky, momentová preťažiteľnosť, krok krokového motora a podobne). Zvyčajne je súbor údajov, ktoré definujú zadanie preurčený, to znamená, že dodržiavanie parametrov jednej triedy je podmienené inou triedou zadaných parametrov, respektíve absolútne dodržanie jedných, vylučuje dodržanie druhých. Jednoducho povedané, jednotlivé parametre uvedené v zadaní sú na sebe navzájom závislé. Robiť výpočet skusmo je zdĺhavé a neefektívne. Dlhoročná prax pri navrhovaní elektrických strojov a získané vedomosti viedli ku spracovaniu postupov a odporúčaní formou empirických vzťahov, tabuliek a grafov, ktoré rešpektujú rôzne parametre strojov, použité materiály, typy elektromechanických aktuátorov podľa ich fyzikálneho princípu pôsobenia, použitia a prevádzkových pomerov strojov, konštrukciu, s cieľom nájsť spôsob a postup, ktorý bude najrýchlejšie a najpravdepodobnejšie viesť k cieľu, k návrhu aktuátora, ktorý vyhovuje zadaniu a normami odporúčaným hodnotám strát, tepelných pomerov a pod. V mnohých prípadoch sú definované rôzne limitujúce podmienky, ktoré treba pri návrhu akceptovať, napr. minimálna cena motora, maximálne možné rozmery, maximálna hmotnosť, definovaná dedičnosť vybraných konštrukčných prvkov pri návrhu radu aktuátorov a pod. V takých to prípadoch je výhodné využiť možnosti výpočtovej techniky. Spracovať návrh aktuátora vo forme programu s využitím princípov metód statickej optimalizácie. 1. OPTIMALIZÁCIA NÁVRHOVÝCH METÓD 1.1 PRINCÍP OPTIMALIZÁCIE Pri formulácii optimalizácie možno vychádzať z teoretického základu, ktorý je napr. uvedený v 1. Pod úlohou optimalizácie rozumieme výber najlepšieho variantu podľa určitého kritéria z množiny možných alebo dovolených variantov. Pri riešení úlohy optimalizácie treba vo všeobecnosti určiť z danej množiny prvkov taký prvok *, v ktorom kritérium optimalizácie vyjadrené účelovou funkciou J J (1) nadobúda extrémnu hodnotu, a to minimum alebo maximum, podľa požiadavky úlohy. Ďalšia konkretizácia všeobecnej úlohy optimalizácie sa zakladá na konkretizácii opisu množiny a účelovej funkcie J. Množina vyjadruje podmienky optimalizácie, obmedzenia kladené na výber prvkov množina prípustných konštrukčných variantov nejakého zariadenia a pod. . Môže to byť napr. z množiny , je zároveň mierou optimálnosti výberu tohto prvku. Hodnoty účelovej funkcie pre rôzne prvky umožňujú tieto Účelová funkcia vyjadruje cieľ optimalizácie a jej hodnota, vypočítaná pre konkrétny prvok ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 127 prvky porovnávať, určovať, ktorý z nich sa viac približuje k optimálnemu. Pri statickej optimalizácii ide o určovanie optimálnych hodnôt určitých meniteľných veličín (parametrov), pri ktorých účelová funkcia nadobúda extrémnu hodnotu. Účelová funkcia sa dá v tomto prípade vyjadriť ako funkcia týchto parametrov. Optimalizačná úloha bude úlohou statickej optimalizácie, ak kritérium optimalizácie je funkcia závislá od hodnôt parametrov J J (a1 , a2 ,...an ) J (a) kde a sme označili vektor parametrov (2) a1 , a2 ,...an . Úlohou statickej optimalizácie je určiť také hodnoty parametrov a1 , a 2 ,...a n alebo súhrnne vektor a* z dovolenej množiny , pri ktorom bude účelová funkcia nadobúdať extrémnu hodnotu, napr. minimum J a min J a : a Keďže (3) max J a min a môžeme v ďalších úvahách vždy predpokladať minimalizáciu kriteriálnej funkcie. Stručne môžeme charakterizovať metódy riešenia úloh statickej optimalizácie nasledovne: 1.1.1 ANALYTICKÉ METÓDY RIEŠENIA ÚLOH STATICKEJ OPTIMALIZÁCIE Riešime úlohu min J a a (4) Podľa spôsobu zadania množiny dovolených vektorov parametrov môžeme úlohy statickej optimalizácie a metódy ich riešenia rozdeliť na tri skupiny: 1. Množina obsahuje všetky reálne vektory. To znamená, že na parametre, od ktorých závisí účelová funkcia, sa nekladú žiadne obmedzenia. 2. Množina je daná systémom rovníc (5) g j a 0, j 1,2,...m n 3. Množina je daná systémom nerovníc (prípadne aj rovníc) g j a 0 j 1,2,...m (6) kde m je ľubovoľné číslo. V prvom prípade ide o bežnú matematickú úlohu nájsť extrém reálnej funkcie n premenných. Nevyhnutnou (ale nie postačujúcou) podmienkou, aby v bode a* bol extrém funkcie stacionárnym bodom, pre ktorý sú splnené rovnice: J a 0, ai alebo i=1,2,...n J a , je, aby bod a* bol (7) grad J a 0 . V prípade obmedzení v tvare rovníc (4) každej rovnici v n-rozmernom priestore parametrov zodpovedá hyperplocha. Extrém funkcie J a hľadáme v prieniku týchto hyperplôch. Počet rovníc m nemá byť väčší ako počet parametrov n. V opačnom prípade úloha buď nemá riešenie, alebo má riešenie len pre špeciálne prípady. Takto formulovanú úlohu nazývame úloha s viazaným extrémom a možno ju riešiť metódou Lagrangeových ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 128 funkcií. Pôvodnú účelovú funkciu J a nahradíme novou –Lagrangeovou funkciou. m Qa, J a i gi a (8) i 1 kde λj sú dodatočné parametre – Lagrangeove multiplikátory. Platí, že extrém funkcie J a na množine danej rovnicami (5) je totožný so sedlovým bodom Lagrangeovej funkcie (8). Pre sedlový bod platia rovnice Qa, 0, ai i 1,2,..., n (9) Qa, 0, j j 1,2,..., m (10) Rovnice (9) a (10) vyjadrujú nevyhnutné podmienky, ktorým má vyhovovať optimálny vektor parametrov a* a vektor Lagrangeových multiplikátorov pri riešení úlohy statickej optimalizácie s obmedzeniami v tvare rovníc (5). Podstatne zložitejšou je úloha statickej optimalizácie pri obmedzeniach v tvare nerovníc (6). Riešenie takýchto úloh vyžaduje osobitné metódy. Pre ne sa zaužíval názov metódy matematického programovania. Najjednoduchšie sa rieši úloha matematického programovania vtedy, ak má účelová funkcia J a absolútny extrém, a to v bode a*, ktorý je z dovolenej množiny . V takom prípade riešenie hľadáme riešením rovníc (7). J a je v bode mimo dovolenej oblasti alebo ak účelová funkcia nemá absolútny extrém, treba hľadať riešenie na hranici množiny . Pre hľadaný optimálny bod a*, v ktorom nadobúda účelová funkcia extrémnu hodnotu na hranici množiny budú splnené V ostatných prípadoch, t. j. ak absolútny extrém účelovej funkcie niektoré z rovníc: g j a * 0 (11) Keby sme vopred vedeli, ktoré sú to rovnice, mohli by sme úlohu riešiť ako v prípade obmedzení v tvare rovníc optimalizáciou Lagrangeovej funkcie (8). Úlohu s obmedzeniami tvaru nerovníc môžeme transformovať na úlohu s obmedzeniami v tvare rovníc aj tak, že namiesto nerovníc (12) g j a 0, j 1,2,..., m definujeme obmedzujúce podmienky rovnicami G j a, u g j a u 2j 0, j 1,2,..., m (13) Taký postup je značne neefektívny, lebo príliš zväčšuje počet neznámych parametrov, a tým aj objem výpočtov. Všeobecný prístup k riešeniu úloh matematického programovania môže vychádzať z poznatkov Kuhna a Tuckera, ktorí zovšeobecnili metódu Lagrangeových funkcií na úlohy s obmedzeniami v tvare nerovníc. Definujeme funkcie G j a 0 G j a g j a pre g j 0 (14) pre g j 0 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 129 Platí, že extrém účelovej funkcie bodom Lagrangeovej funkcie J a na hranici množiny danej nerovnicami (6) je totožný so sedlovým m Qa, J a j G j a (15) j 1 Analytické riešenie úlohy je však teraz sťažené spôsobom definovania funkcií G j a . 1.1.2 METÓDY RIEŠENIA ÚLOHY STATICKEJ OPTIMALIZÁCIE POSTUPNÝM PRIBLIŽOVANÍM K EXTRÉMU Rovnice, ktoré dostávame pri analytických metódach statickej optimalizácie, nie vždy možno riešiť v uzavretom tvare. V praxi sa stretávame aj s takými úlohami optimalizácie, keď je možné určiť len realizovanú hodnotu účelovej funkcie J a , ale nepoznáme jej závislosť od parametrov, alebo sa táto závislosť s časom mení. Vo všetkých týchto prípadoch sa úloha statickej optimalizácie rieši metódami postupného približovania k optimálnemu riešeniu postupnou zmenou vektora parametrov a pri rešpektovaní obmedzení a súčasnom vyhodnocovaní výsledkov. Metódy postupného približovania k extrému rozlišujeme podľa spôsobu určovania smeru, ktorým sa má meniť vektor parametrov a tak, aby sa približoval k optimálnemu a podľa spôsobu realizácie týchto zmien. Podľa spôsobu realizácie zmien vektora parametrov rozlišujeme spojité a diskrétne metódy statickej optimalizácie. Pri spojitých metódach sa vektor parametrov mení spojite. Zaujíma nás, ako určovať, alebo voliť rýchlosť zmeny vektora parametrov da v, dt (16) aby proces optimalizácie bol stabilný a ustálil sa v stacionárnom bode a*, v ktorom je extrém účelovej funkcie Ja . Pre účelovú funkciu, ktorá má v bode a* extrém minima, zvoľme Ľapunovovu funkciu L a J a J a* , (17) ktorá má byť kladne definitná pre celú množinu , s výnimkou stacionárneho bodu. Aby bol proces asymptotický stabilný, musí byť derivácia Ľapunovovej funkcie, podľa času, záporne definitná s výnimkou stacionárneho bodu. To znamená, že v procese optimalizácie má byť stále splnená podmienka pre dJ a T da T grad J a grad J a v0 dt dt (18) a a* (19) Voľbou spôsobu určenia vektora v v každom bode priestoru parametrov a v každom časovom okamihu môžeme vytvárať rôzne algoritmy statickej optimalizácie. Základnou metódou je spojitá gradientová metóda, pri ktorej vektor rýchlosti zmeny parametrov volíme úmerný gradientu účelovej funkcie. Pri hľadaní minima účelovej funkcie vektor rýchlosti zmeny parametrov má opačnú orientáciu ako gradiet účelovej funkcie. da K grad J a dt (20) V procese optimalizácie, podľa vzťahu (20), sa bod a v priestore parametrov pohybuje po trajektórii najstrmšieho klesania účelovej funkcie. Gradientovú metódu môžeme použiť na riešenie úlohy statickej optimalizácie s obmedzeniami v tvare nerovníc ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 130 g j a 0, Pôvodnú účelovú funkciu j 1,2,..., m (21) Ja rozšírime o pokutové funkcie, čím dostaneme novú kriteriálnu funkciu m Qa J a j g j a (22) j 1 kde pre g j a 0 j 0 pre g j a 0 . j 1 Kladné znamienko vo vzťahu platí pre minimalizáciu a záporné pre maximalizáciu účelovej funkcie Rovnica najrýchlejšieho klesania (stúpania), podľa ktorej má prebiehať proces optimalizácie je: m da K grad Qa K grad Qa j grad g j a dt j 1 J a . (23) Horné znamienka sú pre úlohu minimalizácie a dolné pre úlohu maximalizácie. Statická optimalizácia, pri použití číslicových počítačov, prebieha ako diskrétny proces. Vektor parametrov sa mení diskrétne v jednotlivých krokoch a k 1 a k a k (24) Stabilita diskrétneho procesu optimalizácie vyžaduje, aby sa v každom kroku realizovali len také zmeny parametrov, pre ktoré bude splnená podmienka J a k 1 J a k 0 (25) ak sa určuje minimum účelovej funkcie, alebo J ak 1 J ak 0 (26) ak sa určuje maximum účelovej funkcie. Na stabilitu diskrétneho procesu má vplyv tak voľba smeru zmeny vektora parametrov, ako aj veľkosť tejto zmeny v každom kroku. Stručne uvediem niektoré základné metódy diskrétnej statickej optimalizácie. Algoritmus diskrétnej gradientovej metódy je daný vzťahom ak 1 ak K grad J ak (27) Vzťah (27) platí pre minimalizáciu účelovej funkcie. Smer zmeny vektora parametrov je v opačnom smere gradientu účelovej funkcie v príslušnom k-tom bode. Veľkosť zmeny je daná absolútnou hodnotou gradientu a koeficientom K. Od voľby koeficientu K závisí rýchlosť konvergencie a stabilita procesu optimalizácie. Pri Gaussovej – Seidelovej metóde meníme postupne jeden parameter, obyčajne o konštantnú hodnotu, kým hodnoty ostatných parametrov zostávajú nezmenené. Parameter meníme dovtedy, kým platí vzťah (25). Potom meníme tým istým spôsobom ďalší parameter. Proces cyklicky opakujeme pre všetky parametre. V okolí optimálneho bodu môžeme krok zmenšovať, aby sa zvýšila presnosť priblíženia k optimálnemu riešeniu. Prednosti gradientovej a Gaussovej – Seidelovej metódy spája metóda najrýchlejšieho štartu. V začiatočnom bode sa určí smer gradientu. Vektor parametrov sa mení po krokoch v opačnom smere gradientu určeného v začiatočnom bode dovtedy, kým platí vzťah (25). V poslednom bode sa určuje opäť gradient účelovej funkcie. Tým bude daný nový smer zmien vektora parametrov. Proces sa cyklicky opakuje. Ďalšou metódou je metóda náhodných pokusov, ktorá nevyžaduje určovať gradient účelovej funkcie. V začiatočnom bode zmeníme vektor parametrov a k pripočítaním náhodne zvoleného vektora a k : ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 131 ak 1 ak ak . (28) Zistíme, ako sa zmenila účelová funkcia J k J ak 1 J ak . Pri hľadaní minima účelovej funkcie, ak rozdiel (29) J k je záporný, budeme vektor parametrov ďalej meniť ak . Ak je rozdiel J k kladný, budeme meniť vektor parametrov odpočítavaním náhodného vektora ak . V každom kroku zisťujeme platnosť podmienky (25) a vektor postupným pripočítavaním vektora parametrov meníme dovtedy, kým podmienka platí. Keď podmienka (25) neplatí, zmeníme posledný vektor parametrov pripočítaním iného náhodného vektora a postup opakujeme. 1.1.3 LINEÁRNE PROGRAMOVANIE Špeciálnym typom statickej optimalizácie je lineárne programovanie. Vyznačuje sa tým, že účelová funkcia je lineárnou funkciou parametrov n J x c T x ci xi (30) i 1 a množina dovolených parametrov je daná systémom lineárnych nerovníc n a i n ij xi a Tj x b j , j= 1,2, ..., m x j 0, (31) i = 1,2, ..., n (32) Alebo vyjadrené súhrnne vo vektorovom tvare Ax b 0 . (33) Lineárna funkcia (30) nemá lokálny extrém, preto extrém musí v tomto prípade byť na hranici množiny Ω. Množina má tvar mnohostenu a n – rozmernom priestore a je ohraničená rovnicami a Tj x b j j = 1, 2, ..., m (34) Úloha lineárneho programovania predstavuje špecifický typ úlohy statickej optimalizácie, ktorá bola sformulovaná Kolmogorovom. Na jej riešenie môžeme využiť všeobené metódy statickej optimalizácie. Niektoré problémy sa vyznačujú veľkým počtom neznámych veličín a veľkým počtom nerovníc, vyjadrujúcich obmedzenia. Aplikácia všeobecných metód statickej optimalizácie v takých prípadoch nie je efektívna. Lineárnosť úloh umožnila vypracovať špeciálne metódy, ktoré vedú rýchlejšie k výsledku. Najznámejšou je simplexová metóda. Konečným počtom nerovníc je v priestore neznámych veličín vymedzená množina prípustných riešení v tvare mnohostenu a konečným počtom hrán a vrcholov.Metóda spočíva na postupnom pohybe po hranách mnohostena od vrcholu k vrcholu tak, že každé nasledujúce riešenie z hľadiska účelovej funkcie je lepšie ako predchádzajúce. Optimálne riešenie sa dosiahne za konečný počet krokov. Iný variant metódy spočíva v kombinácii gradientovej metódy statickej optimalizácie a pohybu po stenách množiny dovolených riešení. Z určitého východiskového stavu x(0) sa mení vektor x v smere gradientu účelovej funkcie ( ak hľadáme maximum účelovej funkcie), ktorým je vektor c x(1) = K(1) c (35) postupným zväčšovaním kroku K(1), pri ktorej sa jedna z nerovníc zmení na rovnicu. Ostatné nerovnice musia byť splnené. Tak bod x(1) dosiahol prvú stenu dovolenej množiny opísanú niektorou z rovníc a Tj x b j (36) kde j znamená j-tú rovnicu vyplývajúcu zo vzťahu (31), resp.(34). Z dosiahnutého stavu x(1) sa opäť bude meniť ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 132 vektor x v smere gradientu účelovej funkcie, ale po stene, ktorá je opísaná rovnicou (36) až kým sa ďalšia nerovnica nezmení na rovnicu. Gradient účelovej funkcie premietnutý do roviny opísanej vzťahom (36) je grad jJ c(1) c aTjca j aTja j (37) Nové hodnoty premenných sa budú počítať podľa vzťahu aTjca j x(2) x(1) K (2)c(1) x(1) K (2) c T (38) a j a j postupným zväčšovaním kroku K(2) až sa zastupujúci bod x(2) dostane na ďalšiu stenu opísanú rovnicou (36), ale pre iné j. Druhý krok opakujeme až po dosiahnutí extrému účelovej funkcie na dovolenej množine. Pre počet neznámych veličín väčší ako dva, je potrebné metódu modifikovať tak, aby každý pohyb zastupujúceho bodu bol po hranách množiny, to znamená, aby postupne súčasne bolo splnených viac rovníc, až po n rovníc.Gradient po hrane určujeme viacnásobným použitím vzťahu (38) tak, že za vektor c dosadíme vždy novú hodnotu c(k) a za aj vektor poslednej dosiahnutej plochy. Po n krokoch sa dosiahne niektorý vrchol mnohostenu. Tomuto vrcholu zodpovedá bázické riešenie. Ďalší pohyb pri splnení vždy n-1 rovníc bude po hranách od vrcholu k vrcholu až po výsledné riešenie. Tento postup zodpovedá simplexovej metóde. Riešenie sa získa za konečný počet krokov. 2. ROVNICE OPTIMALIZÁCIE Keďže návrh aktuátora vedie k opakovanému výpočtu závislostí medzi hlavnými ukazovateľmi danými formou vzťahov, empirických koeficientov a grafických závislostí, optimálny návrh elektrických strojov je možné chápať ako nájdenie optimálnych parametrov riešením danej sústavy. Výber kritérií optimálnosti závisí od toho, na čo je stroj určený a na požiadavkách, ktoré sú naň kladené. Voľba optimalizačnej funkcie závisí od tých požiadaviek, ktoré pri dodržaní ostatných požadovaných parametrov sú rozhodujúce. Úlohu optimálneho návrhu elektromechanického aktuátora je teda možné si predstaviť ako všeobecnú úlohu statickej optimalizácie, ktorá vedie k nájdeniu minima zvolenej optimalizačnej funkcie pri danom počte nezávisle premenných a funkcií limitujúcich faktorov a obmedzení. 2.1PRÍKLADY OPTIMALIZAČNÝCH FUNKCIÍ 2.1.1PRÍKLAD OPTIMALIZAČNEJ FUNKCIE PRE TUBULÁRNY KROKOVÝ MOTOR Napríklad pri návrhu tubulárneho krokového motora, ak vychádzame z toho, že kritériom optimálneho riešenia návrhu aktuátora, pri dodržaní ostatných zadaných parametrov, sú minimálne rozmery - vonkajší priemer motora Dea dĺžka aktívnej časti aktuátora le, tak môžeme odvodiť nasledovné optimalizačné funkcie: 1.) závislosť počtu zubov pólu na dĺžke aktívnej časti aktuátora le nz= f(le), (39) ktorej tvar je nz l e l p K , (40) 2.) závislosť priemeru kotvy od počtu zubov pólu dt = f(nz), ktorej tvar je (41) K d t2 Ld t M 0 , (42) 3.) závislosť počtu závitov budiacej cievky od priemeru kotvy N = f(dt), ktorej tvar je (43) N Fm k3 , k4 Ik5 Bt dt2 k2 dt k6 (44) 4.) závislosť šírky cievky od priemeru kotvy a počtu zubov jedného pólu bc = f(dt, nz), ktorej tvar je (45) ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 133 bc k12 n z N D , D (46) 5.) závislosť vonkajšieho priemeru od priemeru kotvy výšky budiacej cievky De = f(dt,hc), ktorej tvar je (47) De G F 2k0 , (48) kde D, D’, F, G, K’, K’’, L, M, N’, k0, k2, k4 , k5 , k6 , k12sú parametrezávislé na rozmeroch aktuátora. 2.1.2 PRÍKLAD OPTIMALIZAČNEJ FUNKCIE PRE INDUKČNÉ MOTORY Pri návrhu indukčných motorov môžeme za kritériá optimalizácie zvoliť, podľa požiadaviek na vlastnosti motora napríklad požadovaný menovitý moment motora MN, minimálny možný moment zotrvačnosti J. Potom optimalizačná funkcia má tvar T = f(kD;λ;DE), ktorej tvar je (49) k D6 DE6 K 1 s K 2 s 3 prípadne môže mať Mtvar (50) F k D ,s n (51) TN Tn k D , s n .k M k D , s n . J k D 2.1.3 PRÍKLAD OPTIMALIZAČNEJ FUNKCIE PRE VYSOKO MOMENTOVÝ KROKOVÝ MOTOR Pri návrhu vysoko momentového krokového motora môžeme za kritériá optimalizácia za predpokladu potreby dosiahnutia maximálneho momentu motora T, vziať vŕrtanie motora D, veľkosť vzduchovej medzery a dĺžku motora l. Formálny tvar optimalizačnej funkcie potom je T = f(D,δ,l) a tvar rovnice je nasledovný 1 ce f D , ,l dG f D , ,l . .k 2 . 2 2 Gmax d f D , ,l 2 Ts , f D , ,l (52) 3. ZÁVER V predloženom príspevku sú zhrnuté poznatky a skúsenosti autora získané v rámci prác súvisiacich s vypracovaním princípov optimalizácie návrhových metód elektromechanických akčných členov s využitím informačných technológií. 4. LITERATÚRA [1] BORŠČ, M.; HURTA, F.; VITKO, A. Systems of automatic control, Trenčín : University of Trenčín, 2001, 300 pp, ISBN 80-88914-48-5 (in Slovak) [2] WAGNER, J. Design of chosen electromechanical actuators, Kunovice : Publisher EPI, Ltd., 2008, 133 pp., ISBN 978-80-7314-152-3. (in Slovak) [3] WAGNER, J. Contribution to design of linear stepper motors. Acta Mechanica Slovaca, Košice, 3B/2008, Proceedings of International Conference MMaMS, Volume12., ISSN 1335-2393(in Slovak) [4] KOČIŠ, Š.; WAGNER, J. Linear stepper motor, In: Proceedings „New generation of control and drive systems of robots“, Kočovce, 1989, ZP ČSVTS ZŤS EVÚ Nová Dubnica, p.72 (in Slovak) [5] LOPUCHINA, E. M.; SEMENČUKOV, G. A. Projektirovanije asinchronnych mikrodvigatelej s primenenijem EVM, Vysšaja škola, 1980. [6] WAGNER, J.; MAGA, D.; OPATERNY, J.; GUBA, R.; KUCHTA, J.; RACEK, V. Asynchronous Motor for Diesel-electrical Traction, In: Proceedings of 31st International Intelligent Motion Conference PCIM ´97, June 10-12, 1997, Nurnberg, Germany. [7] WAGNER, J.; KUCHTA, J.; KLEMBAS, R. The Simulation of Operating Characteristics of Tractive Asynchronous Motor, Proceeding of 10th EDPE International Conference Electrical Drives and Power Electronics, Dubrovnik, Croatia, October 1998, pp. 36-41. ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 134 [8] [9] [10] [11] WAGNER, J.; KLEMBAS, R.; MAGA, D.; RÁČEK, V.; KUCHTA, J. Asynchronous Traction Motor, Proceeding of International Workshop on Electrical Machines, Prague, FEE of CTU in Prague, September 1997, pp. 96-98. GVOZDJAK, L.; BORŠČ, M.; VITKO, A. Základy kybernetiky, Bratislava : ALFA, 1990. WAGNER, J.; MAGA, D. FEM Hightorque Stepmotor Design Optimisation, In: Proceedings of 2nd International Conference „Design to manufacture in Modren Industry“, Bled – Maribor, University of Maribor, 1995, pp. 600 – 611. WAGNER, J.; MAGA, D. Vysokomomentový krokový motor, Trenčín : Trenčianska univerzita Alexandra Dubčeka v Trenčíne, 2006, 204 strán, ISBN 80-8075-108-0, EAN 9788080751081. ADRESS: Dr. h. c., doc. Ing. Juraj Wagner, PhD. Evropský polytechnický institute, s.r.o. Gallayova 1, 841 02 Bratislava, tel.: 00421/918884637, fax: 00421/2/64362340, e-mail:[email protected] ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 135 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 136 JMENNÝ REJSTŘÍK A ARTEMENKO, O. .................. 123 M MARČEK, D. ............................ 75 B BARTONĚK, D. ............. 9, 17, 81 O OPATŘILOVÁ, I. ............... 17, 81 OŠMERA, P............................... 89 D DERMEKOVÁ, S. ................ 9, 17 DOSTÁL, P. ............................... 27 P PETRUCHA, J. .......................... 95 Ď ĎUĎÁK, J. ................................. 31 R RUKOVANSKÝ, I. ................. 101 F FALÁT, L. .................................. 37 S SLOVÁČEK, D ....................... 117 G GAŠPAR, G. .............................. 31 Š ŠEDA, M. ................................ 109 H HANULIAK, I. ......................... 43 HUDIK, M. ................................ 51 V VYKLYUK, Y. ........................ 123 W WAGNER, J. .......................... 127 J JANOVIČ, F. .............................. 57 K KEBÍSEK, M. ............................ 31 KEJVALOVÁ, K. ...................... 65 KRATOCHVÍL, O. ................... 27 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 137 ICSC– INTERNATIONAL CONFERENCE ON SOFT COMPUTING APPLIED IN COMPUTER AND ECONOMIC ENVIRONMENTS” EPI Kunovice, Czech Republic. January 20, 2012 138 Title: ICSC 2012 – Tenth International Conference on Soft Computing Applied in Computer and Economic Environments Author: Team of authors Publisher, copyright holders, manufactured: European Polytechnic Institute, Ltd. Osvobození 699, 686 04 Kunovice, Czech Republic Load: 100 pcs Number of pages: 138 Edition: first Release Year: 2012 ISBN 978-80-7314-279-7