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Evolutionary Algorithms

Evolutionary algorithms are bio-inspired algorithms based on Darwin s theory of evolution. They are expected to provide non-optimal but good quality solutions to problems whose resolution is impracticable by exact methods. In six chapters, this book presents the essential knowledge required to efficiently implement evolutionary algorithms. Chapter 1 describes a generic evolutionary algorithm as well as the basic operators that compose it. Chapter 2 is devoted to the solving of continuous optimization problems, without constraint. Three leading approaches are described and compared on a set of test functions. Chapter 3 considers continuous optimization problems with constraints. Various approaches suitable for evolutionary methods are presented. Chapter 4 is related to combinatorial optimization. It provides a catalog of variation operators to deal with order-based problems. Chapter 5 introduces the basic notions required to understand the issue of multi-objective optimization and a variety of approaches for its application. Finally, Chapter 6 describes different approaches of genetic programming able to evolve computer programs in the context of machine learning.
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Table of Contents

Preface xi Chapter 1 Evolutionary Algorithms 1 1.1 From natural evolution to engineering 1 1.2 A generic evolutionary algorithm 3 1.3 Selection operators 5 1.4 Variation operators and representation 21 1.5 Binary representation 25 1.6 The simple genetic algorithm 30 1.7 Conclusion 31 Chapter 2 Continuous Optimization 33 2.1 Introduction 33 2.2 Real representation and variation operators for evolutionary algorithms 35 2.3 Covariance Matrix Adaptation Evolution Strategy 46 2.4 A restart CMA Evolution Strategy 55 2.5 Differential Evolution (DE) 57 2.6 Success-History based Adaptive Differential Evolution (SHADE) 65 2.7 Particle Swarm Optimization 70 2.8 Experiments and performance comparisons 77 2.9 Conclusion 88 2.10 Appendix: set of basic objective functions used for the experiments 89 Chapter 3 Constrained Continuous Evolutionary Optimization 93 3.1 Introduction 93 3.2 Penalization 98 3.3 Superiority of feasible solutions 112 3.4 Evolving on the feasible region 117 3.5 Multi-objective methods 123 3.6 Parallel population approaches 130 3.7 Hybrid methods 132 3.8 Conclusion 132 Chapter 4 Combinatorial Optimization 135 4.1 Introduction 135 4.2 The binary representation and variation operators 140 4.3 Order-based Representation and variation operators 143 4.4 Conclusion 163 Chapter 5 Multi-objective Optimization 165 5.1 Introduction 165 5.2 Problem formalization 166 5.3 The quality indicators 167 5.4 Multi-objective evolutionary algorithms 169 5.5 Methods using a Pareto ranking 169 5.6 Many-objective problems 176 5.7 Conclusion 181 Chapter 6 Genetic Programming for Machine Learning 183 6.1 Introduction 183 6.2 Syntax tree representation 186 6.3 Evolving the syntax trees 187 6.4 GP in action: an introductory example 194 6.5 Alternative Genetic Programming Representations 200 6.6 Example of application: intrusion detection in a computer system 210 6.7 Conclusion 215 Bibliography 217 Index 233

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