Evolutionary Computation 1 Basic Algorithms and Operators EDITORS IN CHIEF Thomas Back¨ Associate Professor of Computer Science, Leiden University, The Netherlands; and Managing Director and Senior Research Fellow, Center for Applied Systems Analysis, Informatik Centrum Dortmund, Germany David B Fogel Executive Vice President and Chief Scientist, Natural Selection Inc., La Jolla, California, USA Zbigniew Michalewicz Professor of Computer Science, University of North Carolina, Charlotte, USA; and Institute of Computer science, Polish Academy of Sciences, Warsaw, Poland EDITORIAL BOARD Peter J Angeline, USA David Beasley, UK Lashon B Booker, USA Kalyanmoy Deb, India Larry J Eshelman, USA Hitoshi Iba, Japan Kenneth E Kinnear Jr, USA Raymond C Paton, UK V William Porto, USA Gunter¨ Rudolph, Germany Robert E Smith, USA William M Spears, USA ADVISORY BOARD Kenneth De Jong, USA Lawrence J Fogel, USA John R Koza, USA Hans-Paul Schwefel, Germany Stewart W Wilson, USA Evolutionary Computation 1 Basic Algorithms and Operators Edited by Thomas Back,¨ David B Fogel and Zbigniew Michalewicz INSTITUTE OF PHYSICS PUBLISHING Bristol and Philadelphia INSTITUTE OF PHYSICS PUBLISHING Bristol and Philadelphia Copyright c 2000 by IOP Publishing Ltd Published by Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, United Kingdom (US Office: The Public Ledger Building, Suite 1035, 150 South Independence Mall West, Philadelphia, PA 19106, USA) All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of IOP Publishing Ltd. British Library Cataloguing-in-Publication Data and Library of Congress Cataloging-in-Publication Data are available ISBN 0 7503 0664 5 PROJECT STAFF Publisher: Nicki Dennis Production Editor: Martin Beavis Production Manager: Sharon Toop Assistant Production Manager: Jenny Troyano Production Controller: Sarah Plenty Electronic Production Manager: Tony Cox Printed in the United Kingdom ∞ ™ The paper used in this publication meets the minimum requirements of American National Standard for Information Sciences – Permanence of Paper for Printed Library Materials, ANSI Z39.48-1984 Contents Preface xiii List of contributors xvii Glossary xxi PART 1 WHY EVOLUTIONARY COMPUTATION? 1 Introduction to evolutionary computation 1 David B Fogel 1.1 Introductory remarks 1 1.2 Optimization 1 1.3 Robust adaptation 2 1.4 Machine intelligence 2 1.5 Biology 2 1.6 Discussion 3 References 3 2 Possible applications of evolutionary computation 4 David Beasley 2.1 Introduction 4 2.2 Applications in planning 4 2.3 Applications in design 6 2.4 Applications in simulation and identification 7 2.5 Applications in control 8 2.6 Applications in classification 9 2.7 Summary 10 References 10 Further reading 18 3 Advantages (and disadvantages) of evolutionary computation over other approaches 20 Hans-Paul Schwefel 3.1 No-free-lunch theorem 20 3.2 Conclusions 21 References 22 v vi Contents PART 2 EVOLUTIONARY COMPUTATION: THE BACKGROUND 4 Principles of evolutionary processes 23 David B Fogel 4.1 Overview 23 References 26 5 Principles of genetics 27 Raymond C Paton 5.1 Introduction 27 5.2 Some fundamental concepts in genetics 27 5.3 The gene in more detail 33 5.4 Options for change 35 5.5 Population thinking 35 References 38 6 A history of evolutionary computation 40 Kenneth De Jong, David B Fogel and Hans-Paul Schwefel 6.1 Introduction 40 6.2 Evolutionary programming 41 6.3 Genetic algorithms 44 6.4 Evolution strategies 48 References 51 PART 3 EVOLUTIONARY ALGORITHMS AND THEIR STANDARD INSTANCES 7 Introduction to evolutionary algorithms 59 Thomas B¨ack 7.1 General outline of evolutionary algorithms 59 References 62 Further reading 62 8 Genetic algorithms 64 Larry J Eshelman 8.1 Introduction 64 8.2 Genetic algorithm basics and some variations 65 8.3 Mutation and crossover 68 8.4 Representation 75 8.5 Parallel genetic algorithms 77 8.6 Conclusion 78 References 78 9 Evolution strategies 81 G¨unter Rudolph 9.1 The archetype of evolution strategies 81 9.2 Contemporary evolution strategies 83 Contents vii 9.3 Nested evolution strategies 86 References 87 10 Evolutionary programming 89 V William Porto 10.1 Introduction 89 10.2 History 90 10.3 Current directions 97 10.4 Future research 100 References 100 Further reading 102 11 Derivative methods in genetic programming 103 Kenneth E Kinnear, Jr 11.1 Introduction 103 11.2 Genetic programming defined and explained 103 11.3 The development of genetic programming 108 11.4 The value of genetic programming 109 References 111 Further reading 112 12 Learning classifier systems 114 Robert E Smith 12.1 Introduction 114 12.2 Types of learning problem 114 12.3 Learning classifier system introduction 117 12.4 ‘Michigan’ and ‘Pitt’ style learning classifier systems 118 12.5 The bucket brigade algorithm (implicit form) 119 12.6 Internal messages 120 12.7 Parasites 120 12.8 Variations of the learning classification system 121 12.9 Final comments 122 References 122 13 Hybrid methods 124 Zbigniew Michalewicz References 126 PART 4 REPRESENTATIONS 14 Introduction to representations 127 Kalyanmoy Deb 14.1 Solutions and representations 127 14.2 Important representations 128 14.3 Combined representations 130 References 131 viii Contents 15 Binary strings 132 Thomas B¨ack References 135 16 Real-valued vectors 136 David B Fogel 16.1 Object variables 136 16.2 Object variables and strategy parameters 137 References 138 17 Permutations 139 Darrell Whitley 17.1 Introduction 139 17.2 Mapping integers to permutations 141 17.3 The inverse of a permutation 141 17.4 The mapping function 142 17.5 Matrix representations 143 17.6 Alternative representations 145 17.7 Ordering schemata and other metrics 146 17.8 Operator descriptions and local search 149 References 149 18 Finite-state representations 151 David B Fogel 18.1 Introduction 151 18.2 Applications 152 References 154 19 Parse trees 155 Peter J Angeline References 158 20 Guidelines for a suitable encoding 160 David B Fogel and Peter J Angeline References 162 21 Other representations 163 Peter J Angeline and David B Fogel 21.1 Mixed-integer structures 163 21.2 Introns 163 21.3 Diploid representations 164 References 164 PART 5 SELECTION 22 Introduction to selection 166 Kalyanmoy Deb Contents ix 22.1 Working mechanisms 166 22.2 Pseudocode 167 22.3 Theory of selective pressure 170 References 171 23 Proportional selection and sampling algorithms 172 John Grefenstette 23.1 Introduction 172 23.2 Fitness functions 172 23.3 Selection probabilities 175 23.4 Sampling 175 23.5 Theory 176 References 180 24 Tournament selection 181 Tobias Blickle 24.1 Working mechanism 181 24.2 Parameter settings 182 24.3 Formal description 182 24.4 Properties 183 References 185 25 Rank-based selection 187 John Grefenstette 25.1 Introduction 187 25.2 Linear ranking 188 25.3 Nonlinear ranking 188 25.4 (µ, λ), (µ + λ) and threshold selection 189 25.5 Theory 190 References 194 26 Boltzmann selection 195 Samir W Mahfoud 26.1 Introduction 195 26.2 Simulated annealing 196 26.3 Working mechanism for parallel recombinative simulated annealing 196 26.4 Pseudocode for a common variation of parallel recombinative simulated annealing 197 26.5 Parameters and their settings 197 26.6 Global convergence theory and proofs 199 References 200 27 Other selection methods 201 David B Fogel 27.1 Introduction 201 27.2 Tournament selection 201 x Contents 27.3 Soft brood selection 202 27.4 Disruptive selection 202 27.5 Boltzmann selection 202 27.6 Nonlinear ranking selection 202 27.7 Competitive selection 203 27.8 Variable lifespan 203 References 204 28 Generation gap methods 205 Jayshree Sarma and Kenneth De Jong 28.1 Introduction 205 28.2 Historical perspective 206 28.3 Steady state and generational evolutionary algorithms 207 28.4 Elitist strategies 210 References 211 29 A comparison of selection mechanisms 212 Peter J B Hancock 29.1 Introduction 212 29.2 Simulations 213 29.3 Population models 214 29.4 Equivalence: expectations and reality 214 29.5 Simulation results 218 29.6 The effects of evaluation noise 222 29.7 Analytic comparison 224 29.8 Conclusions 225 References 225 30 Interactive evolution 228 Wolfgang Banzhaf 30.1 Introduction 228 30.2 History 228 30.3 The problem 229 30.4 The interactive evolution approach 229 30.5 Difficulties 231 30.6 Application areas 231 30.7 Further developments and perspectives 232 References 233 Further reading 234 PART 6 SEARCH OPERATORS 31 Introduction to search operators 235 Zbigniew Michalewicz References 236 Contents xi 32 Mutation operators 237 Thomas B¨ack, David B Fogel, Darrell Whitley and Peter J Angeline 32.1 Binary strings 237 32.2 Real-valued vectors 239 32.3 Permutations 243 32.4 Finite-state machines 246 32.5 Parse trees 248 32.6 Other representations 250 References 252 33 Recombination 256 Lashon B Booker , David B Fogel, Darrell Whitley, Peter J Angeline and A E Eiben 33.1 Binary strings 256 33.2 Real-valued vectors 270 33.3 Permutations 274 33.4 Finite-state machines 284 33.5 Crossover: parse trees 286 33.6 Other representations 289 33.7 Multiparent recombination 289 References 302 34 Other operators 308 Russell W Anderson, David B Fogel and Martin Sch¨utz 34.1 The Baldwin effect 308 34.2 Knowledge-augmented operators 317 34.3 Gene duplication and deletion 319 References 326 Further reading 329 Index 331 Preface The original Handbook of Evolutionary Computation (Back¨ et al 1997) was designed to fulfill the need for a broad-based reference book reflecting the important role that evolutionary computation plays in a variety of disciplines— ranging from the natural sciences and engineering to evolutionary biology and computer sciences.