ABSTRACT
CONTENTS 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
4.1.1 Multiobjective Background Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 4.2 Solving an MOP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
4.2.1 Scalarizing Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.3 Multiobjective Evolutionary Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
4.3.1 Nondominated Sorting Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 4.3.2 Strength Pareto Evolutionary Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 4.3.3 Multiobjective Evolutionary Algorithm Based on Decomposition . . . . . . . . . . . 194 4.3.4 Memetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
4.4 Methods Based on Descent Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 4.5 Gradient-Based Numerical Continuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 4.6 Reference Point Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 4.7 Other Gradient-Based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 4.8 Approaches Based on Nelder and Mead’s Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 208
4.8.1 Multiobjective GA-Simplex Hybrid Algorithm . . . . . . . . . . . . . . . . . . . . . . . 210 4.8.2 Multiobjective Hybrid Particle Swarm Optimization Algorithm . . . . . . . . . . . . 212 4.8.3 Nonlinear Simplex Search Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 214 4.8.4 Hybrid Nondominated Sorting Differential Evolution Algorithm . . . . . . . . . . . 217 4.8.5 Multiobjective Memetic Evolutionary Algorithm Based on Decomposition . . . . 218
4.9 Other Direct Search Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 4.9.1 Multiobjective Meta-Model-Assisted Memetic Algorithm . . . . . . . . . . . . . . . . 221 4.9.2 Hybrid MOEA Based on the S-Metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
4.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
ABSTRACT In this chapter, we present hybridization techniques that allow us to combine evolutionary algorithms with mathematical-programming techniques for solving continuous multiobjective optimization problems. The main motivation for this hybridization is to improve the performance by coupling a global search engine (a multiobjective evolutionary algorithm [MOEA]) with a local search engine (a mathematical-programming technique). The chapter includes a short introduction to multiobjective optimization concepts, as well as some general background about mathematical-programming techniques used for multiobjective optimization and state-of-the-art MOEAs. Also, a general discussion of memetic algorithms (which combine global search engines
with local search engines) is provided. Then, the chapter discusses a variety of hybrid approaches in detail, including combinations of MOEAs with both gradient and non-gradient methods.
