A multiobjective differential evolution algorithm with subpopulation region solution selection for global and local Pareto optimal sets

Abstract

Current multimodal multiobjective optimization (MMO) has mostly focused on locating multiple equivalent global Pareto optimal sets (PSs) or local PSs in the decision space, rarely considering finding both simultaneously. To address this issue, this paper explores a crowded individual activation multiobjective differential evolution algorithm based on subpopulation region solution selection, named CAMODE_SR. In CAMODE_SR, a subpopulation region solution selection mechanism is developed to search for more uniformly distributed global and local Pareto optimal solutions. Specifically, two types of specific neighborhood radii are designed depending on the location information of the Pareto optimal solutions discovered during evolution. The two types of radii construct specific neighborhoods for the global and local optimal solutions to maintain the solutions with better diversity. To improve the exploitation capacity of the population, a crowded individual activation mechanism is proposed by developing an activation function associated with iteration. The activation function activates the crowded individuals in local regions to exploit more superior solutions near global optimal solutions. The proposed CAMODE_SR achieves a good tradeoff between the performance of locating both global and local PSs. Extensive experiments on the CEC 2020 MMO benchmark functions demonstrate that the proposed CAMODE_SR is significantly superior to nine state-of-the-art MMEAs in tackling multimodal multiobjective optimization problems with global and local PSs.