A bi-criterion differential evolution for multimodal multi-objective optimization

Abstract

In this paper, a bi-criterion differential evolution algorithm for multimodal multi-objective optimization is proposed, termed BCDE-MM. A bi-criterion framework based on indicator-based criterion and Pareto criterion is designed. The two criteria are used respectively in the individual and environmental selection to balance the diversity and convergence of the algorithm in objective space. Specifically, a clustering-based indicator fitness assignment scheme is proposed, in which the K-nearest neighbor (KNN) clustering is employed to ensure diversity in the decision space. The indicator-based fitness is assigned in each cluster obtained by KNN based on their distribution in objective space. Consequently, the information of both the decision space and the objective space are considered simultaneously in each subpopulation, which can balance the computing resource assigned to both spaces. In addition, an adaptive mutation method selection strategy is proposed to improve search efficiency. Experimental results verify the effectiveness and superiority of BCDE-MM in solving MMOPs.