Evolutionary Computation with Biogeography-based Optimization

Evolutionary computation algorithms are employed to minimize functions with large number of variables. Biogeography-based optimization (BBO) is an optimization algorithm that is based on the science of biogeography, which researches the migration patterns of species. These migration paradigms provide the main logic behind BBO. Due to the cross-disciplinary nature of the optimization problems, there is a need to develop multiple approaches to tackle them and to study the theoretical reasoning behind their performance. This book explains the mathematical model of BBO algorithm and its variants created to cope with continuous domain problems (with and without constraints) and combinatorial problems.

Table of Contents:
Chapter 1 The Science of Biogeography 1 1.1 Introduction 1 1.2 Island biogeography 3 1.3 Influence factors for biogeography 6 Chapter 2 Biogeography and Biological Optimization 11 2.1 A mathematical model of biogeography 11 2.2 Biogeography as an optimization process 16 2.3 Biological optimization 19 2.3.1 Genetic algorithms 19 2.3.2 Evolution strategies 20 2.3.3 Particle swarm optimization 21 2.3.4 Artificial bee colony algorithm 22 2.4 Conclusion 23 Chapter 3 A Basic BBO Algorithm 25 3.1 BBO definitions and algorithm 25 3.1.1 Migration 26 3.1.2 Mutation 27 3.1.3 BBO implementation 27 3.2 Differences between BBO and other optimization algorithms 35 3.2.1 BBO and genetic algorithms 35 3.2.2 BBO and other algorithms 36 3.3 Simulations 37 3.4 Conclusion 44 Chapter 4 BBO Extensions 45 4.1 Migration curves 45 4.2 Blended migration 49 4.3 Other approaches to BBO 51 4.4 Applications 56 4.5 Conclusion 59 Chapter 5 BBO as a Markov Process 61 5.1 Markov definitions and notations 61 5.2 Markov model of BBO 72 5.3 BBO convergence 79 5.4 Markov models of BBO extensions 90 5.5 Conclusions 99 Chapter 6 Dynamic System Models of BBO 103 6.1 Basic notation 103 6.2 Dynamic system models of BBO 105 6.3 Applications to benchmark problems 119 6.4 Conclusions 122 Chapter 7 Statistical Mechanics Approximations of BBO 123 7.1 Preliminary foundation 123 7.2 Statistical mechanics model of BBO 128 7.2.1 Migration 128 7.2.2 Mutation 134 7.3 Further discussion 141 7.3.1 Finite population effects 141 7.3.2 Separable fitness functions 142 7.4 Conclusions 143 Chapter 8 BBO for Combinatorial Optimization 145 8.1 Traveling salesman problem 147 8.2 BBO for the TSP 148 8.2.1 Population initialization 148 8.2.2 Migration in the TSP 150 8.2.3 Mutation in the TSP 157 8.2.4 Implementation framework 159 8.3 Graph coloring 163 8.4 Knapsack problem 165 8.5 Conclusion 167 Chapter 9 Constrained BBO 169 9.1 Constrained optimization 170 9.2 Constraint-handling methods 172 9.2.1 Static penalty methods 172 9.2.2 Superiority of feasible points 173 9.2.3 The eclectic evolutionary algorithm 174 9.2.4 Dynamic penalty methods 174 9.2.5 Adaptive penalty methods 176 9.2.6 The niched-penalty approach 177 9.2.7 Stochastic ranking 178 9.2.8 ε-level comparisons 178 9.3 BBO for constrained optimization 179 9.4 Conclusion 185 Chapter 10 BBO in Noisy Environments 187 10.1 Noisy fitness functions 188 10.2 Influence of noise on BBO 190 10.3 BBO with re-sampling 193 10.4 The Kalman BBO 196 10.5 Experimental results 199 10.6 Conclusion 201 Chapter 11 Multi-objective BBO 203 11.1 Multi-objective optimization problems 204 11.2 Multi-objective BBO 211 11.2.1 Vector evaluated BBO 211 11.2.2 Non-dominated sorting BBO 213 11.2.3 Niched Pareto BBO 216 11.2.4 Strength Pareto BBO 218 11.3 Real-world applications 223 11.3.1 Warehouse scheduling model 223 11.3.2 Optimization of warehouse scheduling 229 11.4 Conclusion 231 Chapter 12 Hybrid BBO Algorithms 233 12.1 Opposition-based BBO 234 12.1.1 Opposition definitions and concepts 234 12.1.2 Oppositional BBO 236 12.1.3 Experimental results 238 12.2 BBO with local search 240 12.2.1 Local search methods 240 12.2.2 Simulation results 245 12.3 BBO with other EAs 247 12.3.1 Iteration-level hybridization 247 12.3.2 Algorithm-level hybridization 250 12.3.3 Experimental results 254 12.4 Conclusion 256 Appendices 259 Appendix A Unconstrained Benchmark Functions 261 Appendix B Constrained Benchmark Functions 265 Appendix C Multi-objective Benchmark Functions 289 Bibliography 309 Index 325

About the Author :
Haiping Ma, Shangai University, China. Dan Simon, Professor, Cleveland State University, USA.