A dual-archive niche with two-stage directed differential evolution for multimodal multi-objective optimization
摘要
Multimodal Multi-Objective Optimization Problems (MMOPs) refer to situations where there are multiple equivalent Pareto sets corresponding to the same Pareto front. The complexity of solving MMOPs lies in locating multiple equivalent PSs within the decision space while maintaining diversity and convergence in both the decision and objective spaces. To better address this issue, a dual-archive niche approach using two-stage directed differential evolution is proposed, named MMOHCDE_DDM. Firstly, the algorithm leverages the concept of dual archives and introduces affinity propagation clustering for niche differential evolution, automatically generating multiple stable niches. Subsequently, it combines with a competitive particle swarm optimizer to address two solution spaces with different evolutionary requirements. Secondly, by generating multiple subpopulations through affinity propagation clustering, the algorithm employs two distinct mutation strategies to update populations in parallel. This approach enables more effective exploration within niches, effectively enhancing the diversity of both the decision and objective spaces. Furthermore, while the above strategies effectively enhance diversity, they may lead to a loss of convergence. To mitigate this issue and improve convergence, a two-stage directed differential operator is proposed. Introducing a directed differential operator in the later stages of the search provides directed exploration of regions with higher optimality, thereby enhancing convergence. The proposed approach enhances the diversity of both the decision and objective spaces while ensuring convergence in the objective space. The algorithm is compared with various state-of-the-art MMO algorithms on 22 MMO test problems. Experimental results demonstrate that the proposed algorithm outperforms multiple state-of-the-art MMO algorithms in the majority of MMO test problems.