Two-stage species conservation for multimodal multi-objective optimization with local Pareto sets

Abstract

Compared to general multi-objective optimization problems, multimodal multi-objective optimization problems (MMOPs) with local Pareto sets (PSs) must determine multiple global and local PSs simultaneously. Therefore, MMOPs with local PSs are challenging. To resolve this issue, this study proposes a multimodal multi-objective optimization evolutionary algorithm based on two-stage species conservation (MMOEA/TSC). MMOEA/TSC divides the evolutionary process into two stages: diversity-oriented species conservation and convergence-oriented species conservation. The former is aimed at locating promising regions in which global and local PSs may exist. To balance the distribution of solutions, a Gaussian variation strategy is used to iteratively generate diverse offspring in regions that contain the smallest number of solutions. The latter mainly focused on obtaining one PS with good convergence in each promising region. To help the solutions converge to the global and local PSs uniformly, a species stratification strategy was adopted according to the Pareto level of the well-converged solution for each species. The proposed algorithm was compared with seven state-of-the-art algorithms. For the CEC 2020 MMOP test problem set, the experimental results show that MMOEA/TSC has the capacity to find global and local PSs.