A Novel Decomposition-Based Multimodal Multi-objective Evolutionary Algorithm

Abstract

Recently, multimodal multi-objective optimization problems (MMOPs) have got widespread attention, which brings difficulties and challenges to current multi-objective evolutionary algorithms in striking a good balance between diversity in decision space and objective space. This paper proposes a novel decomposition-based multimodal multi-objective evolutionary algorithm, which comprehensively considers diversity in both decision and objective spaces. In environmental selection, a decomposition approach is first used to divide union population into K subregions in objective space and the density-based clustering method is used to divide the union population into different clusters in decision space. Then, the nondominated solutions in the same cluster of each subregion are first selected, and then the remaining ones with good convergence in objective space are further selected to form a temporary population with more than N solutions (N is the population size). Next, temporary population is divided into K subregions by a decomposition approach. The pruning process, which deletes one most crowding solution in the most crowding subregion at each time, will be repeatedly run until there are N solutions left. The experimental results demonstrate that our proposed algorithm can better balance diversity in both decision and objective spaces on solving MMOPs.