Meta-heuristic and Evolutionary Algorithms for Engineering Optimization

Preface xv About the Authors xvii List of Figures xix 1 Overview of Optimization 1 Summary 1 1.1 Optimization 1 1.1.1 Objective Function 2 1.1.2 Decision Variables 2 1.1.3 Solutions of an Optimization Problem 3 1.1.4 Decision Space 3 1.1.5 Constraints or Restrictions 3 1.1.6 State Variables 3 1.1.7 Local and Global Optima 4 1.1.8 Near?-Optimal Solutions 5 1.1.9 Simulation 6 1.2 Examples of the Formulation of Various Engineering Optimization Problems 7 1.2.1 Mechanical Design 7 1.2.2 Structural Design 9 1.2.3 Electrical Engineering Optimization 10 1.2.4 Water Resources Optimization 11 1.2.5 Calibration of Hydrologic Models 13 1.3 Conclusion 15 2 Introduction to Meta?-Heuristic and Evolutionary Algorithms 17 Summary 17 2.1 Searching the Decision Space for Optimal Solutions 17 2.2 Definition of Terms of Meta?-Heuristic and Evolutionary Algorithms 21 2.2.1 Initial State 21 2.2.2 Iterations 21 2.2.3 Final State 21 2.2.4 Initial Data (Information) 21 2.2.5 Decision Variables 22 2.2.6 State Variables 23 2.2.7 Objective Function 23 2.2.8 Simulation Model 24 2.2.9 Constraints 24 2.2.10 Fitness Function 24 2.3 Principles of Meta?-Heuristic and Evolutionary Algorithms 25 2.4 Classification of Meta?-Heuristic and Evolutionary Algorithms 27 2.4.1 Nature?-Inspired and Non?-Nature?-Inspired Algorithms 27 2.4.2 Population?-Based and Single?-Point Search Algorithms 28 2.4.3 Memory?-Based and Memory?-Less Algorithms 28 2.5 Meta?-Heuristic and Evolutionary Algorithms in Discrete or Continuous Domains 28 2.6 Generating Random Values of the Decision Variables 29 2.7 Dealing with Constraints 29 2.7.1 Removal Method 30 2.7.2 Refinement Method 30 2.7.3 Penalty Functions 31 2.8 Fitness Function 33 2.9 Selection of Solutions in Each Iteration 33 2.10 Generating New Solutions 34 2.11 The Best Solution in Each Algorithmic Iteration 35 2.12 Termination Criteria 35 2.13 General Algorithm 36 2.14 Performance Evaluation of Meta?-Heuristic and Evolutionary Algorithms 36 2.15 Search Strategies 39 2.16 Conclusion 41 References 41 3 Pattern Search 43 Summary 43 3.1 Introduction 43 3.2 Pattern Search (PS) Fundamentals 44 3.3 Generating an Initial Solution 47 3.4 Generating Trial Solutions 47 3.4.1 Exploratory Move 47 3.4.2 Pattern Move 49 3.5 Updating the Mesh Size 50 3.6 Termination Criteria 50 3.7 User?-Defined Parameters of the PS 51 3.8 Pseudocode of the PS 51 3.9 Conclusion 52 References 52 4 Genetic Algorithm 53 Summary 53 4.1 Introduction 53 4.2 Mapping the Genetic Algorithm (GA) to Natural Evolution 54 4.3 Creating an Initial Population 56 4.4 Selection of Parents to Create a New Generation 56 4.4.1 Proportionate Selection 57 4.4.2 Ranking Selection 58 4.4.3 Tournament Selection 59 4.5 Population Diversity and Selective Pressure 59 4.6 Reproduction 59 4.6.1 Crossover 60 4.6.2 Mutation 62 4.7 Termination Criteria 63 4.8 User?- Defined Parameters of the GA 63 4.9 Pseudocode of the GA 64 4.10 Conclusion 65 References 65 5 Simulated Annealing 69 Summary 69 5.1 Introduction 69 5.2 Mapping the Simulated Annealing (SA) Algorithm to the Physical Annealing Process 70 5.3 Generating an Initial State 72 5.4 Generating a New State 72 5.5 Acceptance Function 74 5.6 Thermal Equilibrium 75 5.7 Temperature Reduction 75 5.8 Termination Criteria 76 5.9 User?- Defined Parameters of the SA 76 5.10 Pseudocode of the SA 77 5.11 Conclusion 77 References 77 6 Tabu Search 79 Summary 79 6.1 Introduction 79 6.2 Tabu Search (TS) Foundation 80 6.3 Generating an Initial Searching Point 82 6.4 Neighboring Points 82 6.5 Tabu Lists 84 6.6 Updating the Tabu List 84 6.7 Attributive Memory 85 6.7.1 Frequency?-Based Memory 85 6.7.2 Recency?-Based Memory 85 6.8 Aspiration Criteria 87 6.9 Intensification and Diversification Strategies 87 6.10 Termination Criteria 87 6.11 User?- Defined Parameters of the TS 87 6.12 Pseudocode of the TS 88 6.13 Conclusion 89 References 89 7 Ant Colony Optimization 91 Summary 91 7.1 Introduction 91 7.2 Mapping Ant Colony Optimization (ACO) to Ants' Foraging Behavior 92 7.3 Creating an Initial Population 94 7.4 Allocating Pheromone to the Decision Space 96 7.5 Generation of New Solutions 98 7.6 Termination Criteria 99 7.7 User?- Defined Parameters of the ACO 99 7.8 Pseudocode of the ACO 100 7.9 Conclusion 100 References 101 8 Particle Swarm Optimization 103 Summary 103 8.1 Introduction 103 8.2 Mapping Particle Swarm Optimization (PSO) to the Social Behavior of Some Animals 104 8.3 Creating an Initial Population of Particles 107 8.4 The Individual and Global Best Positions 107 8.5 Velocities of Particles 109 8.6 Updating the Positions of Particles 110 8.7 Termination Criteria 110 8.8 User?- Defined Parameters of the PSO 110 8.9 Pseudocode of the PSO 111 8.10 Conclusion 112 References 112 9 Differential Evolution 115 Summary 115 9.1 Introduction 115 9.2 Differential Evolution (DE) Fundamentals 116 9.3 Creating an Initial Population 118 9.4 Generating Trial Solutions 119 9.4.1 Mutation 119 9.4.2 Crossover 119 9.5 Greedy Criteria 120 9.6 Termination Criteria 120 9.7 User?-Defined Parameters of the DE 120 9.8 Pseudocode of the DE 121 9.9 Conclusion 121 References 121 10 Harmony Search 123 Summary 123 10.1 Introduction 123 10.2 Inspiration of the Harmony Search (HS) 124 10.3 Initializing the Harmony Memory 125 10.4 Generating New Harmonies (Solutions) 127 10.4.1 Memory Strategy 127 10.4.2 Random Selection 128 10.4.3 Pitch Adjustment 129 10.5 Updating the Harmony Memory 129 10.6 Termination Criteria 130 10.7 User?- Defined Parameters of the HS 130 10.8 Pseudocode of the HS 130 10.9 Conclusion 131 References 131 11 Shuffled Frog?-Leaping Algorithm 133 Summary 133 11.1 Introduction 133 11.2 Mapping Memetic Evolution of Frogs to the Shuffled Frog Leaping Algorithm (SFLA) 134 11.3 Creating an Initial Population 137 11.4 Classifying Frogs into Memeplexes 137 11.5 Frog Leaping 138 11.6 Shuffling Process 140 11.7 Termination Criteria 141 11.8 User?-Defined Parameters of the SFLA 141 11.9 Pseudocode of the SFLA 141 11.10 Conclusion 142 References 142 12 Honey?-Bee Mating Optimization 145 Summary 145 12.1 Introduction 145 12.2 Mapping Honey?-Bee Mating Optimization (HBMO) to the Honey?- Bee Colony Structure 146 12.3 Creating an Initial Population 148 12.4 The Queen 150 12.5 Drone Selection 150 12.5.1 Mating Flights 151 12.5.2 Trial Solutions 152 12.6 Brood (New Solution) Production 152 12.7 Improving Broods (New Solutions) by Workers 155 12.8 Termination Criteria 156 12.9 User?-Defined Parameters of the HBMO 156 12.10 Pseudocode of the HBMO 156 12.11 Conclusion 158 References 158 13 Invasive Weed Optimization 163 Summary 163 13.1 Introduction 163 13.2 Mapping Invasive Weed Optimization (IWO) to Weeds' Biology 164 13.3 Creating an Initial Population 167 13.4 Reproduction 167 13.5 The Spread of Seeds 168 13.6 Eliminating Weeds with Low Fitness 169 13.7 Termination Criteria 170 13.8 User?- Defined Parameters of the IWO 170 13.9 Pseudocode of the IWO 170 13.10 Conclusion 171 References 171 14 Central Force Optimization 175 Summary 175 14.1 Introduction 175 14.2 Mapping Central Force Optimization (CFO) to Newtons Gravitational Law 176 14.3 Initializing the Position of Probes 177 14.4 Calculation of Accelerations 180 14.5 Movement of Probes 181 14.6 Modification of Deviated Probes 181 14.7 Termination Criteria 182 14.8 User?-Defined Parameters of the CFO 182 14.9 Pseudocode of the CFO 183 14.10 Conclusion 183 References 183 15 Biogeography?-Based Optimization 185 Summary 185 15.1 Introduction 185 15.2 Mapping Biogeography?-Based Optimization (BBO) to Biogeography Concepts 186 15.3 Creating an Initial Population 188 15.4 Migration Process 189 15.5 Mutation 191 15.6 Termination Criteria 192 15.7 User?- Defined Parameters of the BBO 192 15.8 Pseudocode of the BBO 193 15.9 Conclusion 193 References 194 16 Firefly Algorithm 195 Summary 195 16.1 Introduction 195 16.2 Mapping the Firefly Algorithm (FA) to the Flashing Characteristics of Fireflies 196 16.3 Creating an Initial Population 198 16.4 Attractiveness 199 16.5 Distance and Movement 199 16.6 Termination Criteria 200 16.7 User?-Defined Parameters of the FA 200 16.8 Pseudocode of the FA 201 16.9 Conclusion 201 References 201 17 Gravity Search Algorithm 203 Summary 203 17.1 Introduction 203 17.2 Mapping the Gravity Search Algorithm (GSA) to the Law of Gravity 204 17.3 Creating an Initial Population 205 17.4 Evaluation of Particle Masses 207 17.5 UpdatingVelocities and Positions 207 17.6 Updating Newton's Gravitational Factor 208 17.7 Termination Criteria 209 17.8 User?- Defined Parameters of the GSA 209 17.9 Pseudocode of the GSA 209 17.10 Conclusion 210 References 210 18 Bat Algorithm 213 Summary 213 18.1 Introduction 213 18.2 Mapping the Bat Algorithm (BA) to the Behavior of Microbats 214 18.3 Creating an Initial Population 215 18.4 Movement of Virtual Bats 217 18.5 Local Search and Random Flying 218 18.6 Loudness and Pulse Emission 218 18.7 Termination Criteria 219 18.8 User?-Defined Parameters of the BA 219 18.9 Pseudocode of the BA 219 18.10 Conclusion 220 References 220 19 Plant Propagation Algorithm 223 Summary 223 19.1 Introduction 223 19.2 Mapping the Natural Process to the Planet Propagation Algorithm (PPA) 223 19.3 Creating an Initial Population of Plants 226 19.4 Normalizing the Fitness Function 226 19.5 Propagation 227 19.6 Elimination of Extra Solutions 228 19.7 Termination Criteria 228 19.8 User?-Defined Parameters of the PPA 228 19.9 Pseudocode of the PPA 229 19.10 Conclusion 230 References 230 20 Water Cycle Algorithm 231 Summary 231 20.1 Introduction 231 20.2 Mapping the Water Cycle Algorithm (WCA) to the Water Cycle 232 20.3 Creating an Initial Population 233 20.4 Classification of Raindrops 235 20.5 Streams Flowing to the Rivers or Sea 236 20.6 Evaporation 237 20.7 Raining Process 238 20.8 Termination Criteria 239 20.9 User?-Defined Parameters of the WCA 239 20.10 Pseudocode of the WCA 239 20.11 Conclusion 240 References 240 21 Symbiotic Organisms Search 241 Summary 241 21.1 Introduction 241 21.2 Mapping Symbiotic Relations to the Symbiotic Organisms Search (SOS) 241 21.3 Creating an Initial Ecosystem 242 21.4 Mutualism 244 21.5 Commensalism 245 21.6 Parasitism 245 21.7 Termination Criteria 246 21.8 Pseudocode of the SOS 246 21.9 Conclusion 247 References 247 22 Comprehensive Evolutionary Algorithm 249 Summary 249 22.1 Introduction 249 22.2 Fundamentals of the Comprehensive Evolutionary Algorithm (CEA) 250 22.3 Generating an Initial Population of Solutions 253 22.4 Selection 253 22.5 Reproduction 255 22.5.1 Crossover Operators 255 22.5.2 Mutation Operators 261 22.6 Roles of Operators 262 22.7 Input Data to the CEA 263 22.8 Termination Criteria 264 22.9 Pseudocode of the CEA 265 22.10 Conclusion 265 References 266 Wiley Series in Operations Research and Management Science 267 Index 269