Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization

Abstract

Evolutionary algorithms (EAs) have been recognized to be well suited for multiobjective (MO) optimization because they can evolve a set of nondominated individuals distributed along the Pareto front. These methods, however, need to "guess" for an optimal constant population size in order to discover the usually sophisticated tradeoff surface. This paper addresses the issue by presenting a novel incrementing multiobjective evolutionary algorithm (IMOEA) with dynamic population size that is computed adaptively according to the online discovered tradeoff surface and its desired population distribution density. It incorporates the method of fuzzy boundary local perturbation with interactive local fine tuning for broader neighborhood exploration. This achieves better convergence as well as discovering any gaps or missing tradeoff regions at each generation. Other advanced features include a proposed preserved strategy to ensure better stability and diversity of the Pareto front and a convergence representation based on the concept of online population domination to provide useful information such as stopping criteria or optimization performance of the evolution. Extensive simulations are performed on two benchmark and one practical engineering design problems and their performances are compared both quantitatively and statistically with other MO optimization methods. Each of the proposed features in IMOEA is also examined explicitly to illustrate their usefulness in MO optimization.