FUZZY EVOLUTIONARY COMPUTATION FUZZY EVOLUTIONARY COMPUTATION edited by Witold Pedrycz The University ofM anitoba Winnipeg, Manitoba, Canada ., 111.. • SPRINGER SCIENCE+BUSlNESS MEDIA, LLC ISBN 978-1-4613-7811-2 ISBN 978-1-4615-6135-4 (eBook) DOI 10.1007/978-1-4615-6135-4 Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress. Copyright © 1997 by Springer Science+Business Media New York Origina1ly published by Kluwer Academic Publishers in 1997 Softcover reprint of the hardcover 1s t edition 1997 AH rights reserved. No part ofthis publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission ofthe publisher, Springer Science+Business Media, LLC. Printed on acid-free paper. CONTENTS EDITOR'S PREFACE X111 PART 1: FUNDAMENTALS 1.1. EVOLUTIONARY ALGORITHMS Z Michalewicz, R. Hinterding, M. Michalewicz 1. INTRODUcnON 3 2. 4 EVOLUTIONARYCO~ATION 3. MAIN PARADIGMS OF EVOLUTIONARY CO~ATION 7 4. ADAPTING ALGORITIIM TO THE PROBLEM 16 5. DISCUSSION 22 6. REFERENCES 23 1.2. ON THE COMBINATION OF FUZZY LOGIC AND EVOLUTIONARY COMPUTATION: A SHORT REVIEW AND BIBLIOGRAPHY o. Cordon, F. Herrera, M. Lozano 1. INTRODUcnON 33 2. FUZZY GENETIC ALGORITIIMS 35 3. FUZZY CLUS1ERING 37 4. FUZZY OPTIMIZATION 37 5. FUZZY NEURAL NETWORKS 39 6. FUZZY RELATIONAL EQUATIONS 40 7. FUZZY EXPERT SYSTEMS 41 8. FUZZY INFORMATION RETRIEV AL 42 vi 9. FUZZY DECISION MAKING, FINANCIAL, AND ECONOMIC MODELS 42 10. FUZZY REGRESSION ANALYSIS 43 11. FUZZY PATIERN RECOGNITION AND IMAGE PROCESSING 44 12. FUZZY CLASSIFICATION -CONCEPT LEARNING 45 13. GENETIC FUZZY RULE BASED CONfROL SYSTEMS 46 14. FUZZY LOGIC MISCELLANEOUS 55 15. FUZZY LOGIC -GENETIC ALGORITIIMS FRAMEWORK 56 1.3. FUZZYIMUL TIOBJECTIVE GENETIC SYSTEMS FOR INTELLIGENT SYSTEMS DESIGN TOOLS AND COMPONENTS M. A. Lee, H. Esbensen 1. INTRODUCTION 57 2. MULTIOBffiCTIVEEVOLUTIONARYALGORITIIMS 58 3. GENETIC DESIGN OF FUZZY SYSTEMS 60 4. FUZZY -GENETIC ALGORITIIMS 66 5. SUMMARY, CONCLUSIONS, AND EXTENSIONS 76 6. EXERCISES 77 7. ACKNOWLEDGMENfS 77 8. REFERENCES AND RELA1ED PUBLICATIONS 77 PART 2: METHODOLOGY AND ALGORITHMS 2.1. GA ALGORITHMS IN INTELLIGENT ROBOTS T. Fukuda, N. Kubota, T. Arakawa 1. INTRODUCTION 81 2. GENETIC ALGORITHMS FüR INTELLIGENT ROBOT 83 3. HIERARCHICAL TRA.JECTORY PLANNING FüR ROBOT MANIPULATORS 90 4. NATURAL MOTION PLANNING FüR BIPED LOCOMOTION ROBOT 97 5. SUMMARY 103 vii 6. EXERCISE 104 7. REFERENCES 104 2.2. DEVELOPMENT OF IF-THEN RULES WITH THE USE OF DNA CODING T. Furuhashi 1. lNTRODUCTION 107 2. DNA CODING METHOD 108 3. PROBLEM FORMULATION FOR KNOWLEDGE ACQUISITION 112 4. APPLICATION OFDNA CODING METHOD 113 5. SIMULATIONS 116 6. CONCLUSIONS 123 7. REFERENCES 124 8. PROBLEMS 125 2.3. GENETIC-ALGORITHM-BASED APPROACHES TO CLASSIFICATION PROBLEMS H.Ishibuch~ T. Murata, T. Nakashima 1. INTRODUCTION 127 2. FUZZY RULE GENERATION AND FUZZY REASONING 130 3. GENETIC ALGORITHM-BASED RULE SELECfION 135 4. HANDLING OF HIGH-DIMENSIONAL PROBLEMS 145 5. CONCLUSION 148 6. EXERCISES 149 7. REFERENCES 150 vüi 2.4. MULTIOBJECTIVE FUZZY SATISFICING METHODS FOR 0-1 KNAPSACK PROBLEMS mROUGH GENETIC ALGORITHMS M. Sakawa, T. Shibano 1. INTRODUenON 156 2. FUZZY PROORAMMING 157 3. GENETIC ALGORmlMS 159 4. HOW TO EV ALUA1E GA'S PERFORMANCE 161 5. NUMERICAL EXAMPLES 163 6. GENETIC ALGORmlMS WITII OOUBLE STRlNGS 163 7. INTERACTIVE RJZZY SATISFICING METIlODS 168 8. MODIFICATION OF GENETIC ALGORTI1IMS 173 9. CONCLUSIONS 174 10. PROBLEMS 175 11. REFERENCES 176 2.5. MULTIS TAGE EVOLUTIONARY OPTIMIZATION OF FUZZY SYSTEMS - APPLICATION TO OPTIMAL FUZZY CONTROL J. Kacprzyk 1. INTRODUCTION 179 2. MULTISTAGE RJzzy CONTROL IN THE SEITING OF BELLMAN AND ZADEH 182 3. MULTIS TAGE RJzzy CONTROL 184 4. A GENETIC ALGORTI1IM FüR THE SOLUTION OF TIlE MULTIS TAGE FUZZY CONTROL PROBLEM WITII A FUZZY SYS1EM UNDER CONTROL 190 5. CONCLUDING REMARKS 195 6. BIBLIOORAPHY 196 ix 2.6. EVOLUTIONARY LEARNING IN NEURAL FUZZY CONTROL SYSTEMS D. A. Linkens, H. O. Nyongesa 1. EVOLUTIONARY NEURAL FUZZY SYSlEMS: AN OVERVIEW 199 2. FUZZY SYSlEMS REVIEW 201 3. NEURAL NETWORKS REVIEW 204 4. GENETIC AND EVOLUTIONARY ALGORmlMS REVIEW 206 5. INTEGRATED NEURAL FUZZY SYSlEMS 208 6. EVOLUTIONARY NEURAL FUZZY SYSlEMS 210 7. AN APPLICATION CASE STUDY 213 8. CONCLUSIONS AND OUILOOK 217 9. REFERENCES 221 2.7. STABLE IDENTIFICATION AND ADAPTIVE CONTROL . A DYNAMIC FUZZY LOGIC SYSTEM APPROACH G. Vukovich, I.X. Lee 1. INTRODUCTION 224 2. DESCRIPI10N OF DYNAMIC FUZZY LOGIC SYSlEM 225 3. STABLE IDENTIFICATION: A DFLS BASED ALGORITIIM 229 4. DFLS BASED ADAPTIVE CONTROL AND STABILITY PROPERTIES 231 5. ILLUSTRATIVE APPLICATIONS 235 6. CONCLUSIONS 239 7. REFERENCES 241 8. APPENDIX -PROOF OF TIIEOREM 1 241 9. PROBLEMS 248 x 2.8. EVOLUTIONARY BASED LEARNING OF FUZZY CONTROLLERS L Magdalena, J. R. Velasco 1. INTRODUCTION 249 2. nIE LEARNING PROCESS 250 3. WORKING ON A STRUenJRED KNOWLEDGE BASE 252 4. LEARNING PARTS OF nIE KNOWLEDGE BASE 254 5. GLOBAL LEARNING 258 6. AN EVOLUTIONARY FUZZY CONTROLLER 261 7. CONCLUSIONS 265 8. EXERCISES 265 9. REFERENCES 266 2.9. GA-BASED GENERATION OF FUZZY RULES o. Nelles 1. INTRODUCTION 269 2. FUZZY SYSlEMS 269 3. OPTIMIZATION OF FUZZY SYSlEMS 274 4. APPROACHES FOR OPTIMIZATION OF FUZZY SYS1EMS 278 5. OVERCOMING nIE "CURSE OF DIMENSIONALITY" 281 6. GENETIC ALGORITHMS FOR FUZZY RULE GENERATION 282 7. COMBINATION OF A GENETIC ALGORITHM AND CLASSICAL OPTIMIZATION 1ECHNIQUES FOR FUZZY RULE GENERATION 285 8. APPLICATION EXAMPLE 289 9. CONCLUSIONS 292 10. PROBLEMS 292 11. REFERENCES 293 xi PART 3: BIBLIOGRAPHY 3.1. AN INDEXED BmLIOGRAPHY OF GENETIC ALGORITHMS WITH FUZZY LOGIC J. T. Alander 1. INTRODUCTION 299 2. SUBJECTS 300 3. REFERENCES 302 SUBJECT INDEX 319