Dual-space distribution metric-based evolutionary algorithm for multimodal multi-objective optimization

Multimodal multi-objective optimization problems (MMOPs) are characterized by having multiple global or local Pareto solution sets. In most of multimodal multi-objective evolutionary algorithms, the distribution of population in objective space and decision space cannot be taken into account, simultaneously. In this paper, an innovative evolutionary algorithm based on dual-space distribution metric for multimodal multi-objective optimization (DsDMEA) is designed to solve this problem. Specifically, the two enhanced performance metrics are coupled together as a single dual-space distribution metric (DsDM) serving as the criterion for environmental selection. DsDMEA explores solutions on Pareto front and Pareto solutions sets that are not associated with the reference point, which show limited contributions to the distribution in dual spaces. Then DsDMEA removes any bi-noncontributing solutions using DsDM during environmental selection until the population size is met. This achieves a balance between the distribution of solutions and convergence in decision space. At the same time, this paper introduces a novel fitness computation method, enabling the precise localization of local Pareto fronts within the population. Finally, eight state-of-the-art multimodal multi-objective evolutionary algorithms are adopted to make a comparison on two types of benchmark to verify the performance of the DsDMEA. The experimental results demonstrated the DsDMEA effectiveness in solving MMOPs with local problems and traditional MMOPs.