Practical genetic algorithms

1 Introduction to Optimization 1 1.1 Finding the Best Solution 1 1.1.1 What Is Optimization? 2 1.1.2 Root Finding versus Optimization 3 1.1.3 Categories of Optimization 3 1.2 Minimum-Seeking Algorithms 5 1.2.1 Exhaustive Search 5 1.2.2 Analytical Optimization 7 1.2.3 Nelder-Mead Downhill Simplex Method 10 1.2.4 Optimization Based on Line Minimization 13 1.3 Natural Optimization Methods 18 1.4 Biological Optimization: Natural Selection 19 1.5 The Genetic Algorithm 22 Bibliography 24 Exercises 25 2 The Binary Genetic Algorithm 27 2.1 Genetic Algorithms: Natural Selection on a Computer 27 2.2 Components of a Binary Genetic Algorithm 28 2.2.1 Selecting the Variables and the Cost Function 30 2.2.2 Variable Encoding and Decoding 32 2.2.3 The Population 36 2.2.4 Natural Selection 36 2.2.5 Selection 38 2.2.6 Mating 41 2.2.7 Mutations 43 2.2.8 The Next Generation 44 2.2.9 Convergence 47viii CONTENTS 2.3 A Parting Look 47 Bibliography 49 Exercises 49 3 The Continuous Genetic Algorithm 51 3.1 Components of a Continuous Genetic Algorithm 52 3.1.1 The Example Variables and Cost Function 52 3.1.2 Variable Encoding, Precision, and Bounds 53 3.1.3 Initial Population 54 3.1.4 Natural Selection 54 3.1.5 Pairing 56 3.1.6 Mating 56 3.1.7 Mutations 60 3.1.8 The Next Generation 62 3.1.9 Convergence 64 3.2 A Parting Look 65 Bibliography 65 Exercises 65 4 Basic Applications 67 4.1 “Mary Had a Little Lamb” 67 4.2 Algorithmic Creativity—Genetic Art 71 4.3 Word Guess 75 4.4 Locating an Emergency Response Unit 77 4.5 Antenna Array Design 81 4.6 The Evolution of Horses 86 4.5 Summary 92 Bibliography 92 5 An Added Level of Sophistication 95 5.1 Handling Expensive Cost Functions 95 5.2 Multiple Objective Optimization 97 5.2.1 Sum of Weighted Cost Functions 99 5.2.2 Pareto Optimization 99 5.3 Hybrid GA 101 5.4 Gray Codes 104 5.5 Gene Size 106 5.6 Convergence 107 5.7 Alternative Crossovers for Binary GAs 110 5.8 Population 117 5.9 Mutation 121 5.10 Permutation Problems 124 5.11 Selecting GA Parameters5.12 Continuous versus Binary GA 135 5.13 Messy Genetic Algorithms 136 5.14 Parallel Genetic Algorithms 137 5.14.1 Advantages of Parallel GAs 138 5.14.2 Strategies for Parallel GAs 138 5.14.3 Expected Speedup 141 5.14.4 An Example Parallel GA 144 5.14.5 How Parallel GAs Are Being Used 145 Bibliography 145 Exercises 148 6 Advanced Applications 151 6.1 Traveling Salesperson Problem 151 6.2 Locating an Emergency Response Unit Revisited 153 6.3 Decoding a Secret Message 155 6.4 Robot Trajectory Planning 156 6.5 Stealth Design 161 6.6 Building Dynamic Inverse Models—The Linear Case 165 6.7 Building Dynamic Inverse Models—The Nonlinear Case 170 6.8 Combining GAs with Simulations—Air Pollution Receptor Modeling 175 6.9 Optimizing Artificial Neural Nets with GAs 179 6.10 Solving High-Order Nonlinear Partial Differential Equations 182 Bibliography 184 7 More Natural Optimization Algorithms 187 7.1 Simulated Annealing 187 7.2 Particle Swarm Optimization (PSO) 189 7.3 Ant Colony Optimization (ACO) 190 7.4 Genetic Programming (GP) 195 7.5 Cultural Algorithms 199 7.6 Evolutionary Strategies 199 7.7 The Future of Genetic Algorithms 200 Bibliography 201 Exercises