Multi-Objective Optimization Using Evolutionary AlgorithmsEvolutionary algorithms are relatively new, but very powerful techniques used to find solutions to many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run.
The integrated presentation of theory, algorithms and examples will benefit those working and researching in the areas of optimization, optimal design and evolutionary computing. This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study. |
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best non-dominated better calculated choose chosen constraint violation convergence convex corresponding created crossover operator decision variable space discussed distance distribution diversity dominated solutions elite elitist equation Euclidean distance evaluated evolution strategy evolutionary algorithms Evolutionary Computation f₁ feasible solution fitness values genetic algorithm genetic operations goal programming goal programming problem hypercube infeasible solutions local search mating pool maximum metric Minimize minimum MOEA multi-objective optimization problem mutation operator niche count non-dominated front non-dominated set nonconvex NPGA NSGA NSGA-II number of solutions objective function values objective space obtained non-dominated solutions obtained solutions offspring population optimal solutions optimum Oshare parameter parent solutions Pareto Pareto-optimal region Pareto-optimal set Pareto-optimal solutions performed population members procedure random real-parameter schema search space selection operator set of solutions shown in Figure shows simulation solving SPEA Step strategy string subpopulation suggested technique test problems tournament selection trade-off solutions true Pareto-optimal front w₁ WBGA weight vector