A niching-based nondominated sorting for multimodal multiobjective optimization with local pareto fronts

In multimodal multiobjective optimization problems (MMOPs), there may be local Pareto optimal solutions (PSs). Finding both global PS and local PS simultaneously can provide additional options for decision makers. However, since individuals on the global Pareto front (PF) dominate individuals on the local PF, traditional multimodal multiobjective evolutionary algorithms (MMEAs) cannot effectively handle MMOPs with local PF (MMOPLs). In this paper, we improve our previous dynamic-niching-based Pareto domination (DNPD) approach to search for local Pareto optimal solutions. The new version is called niching-based non-dominated sorting (NNSL). There are two improvements to NNSL. First, the dynamic niche is changed to a fixed niche increase the diversity of the population. Second, individuals with poor convergence in the non-dominated layer are deleted to ensure the convergence of the population. NNSL can be combined with Pareto dominance-based algorithms. We apply NNSL to solve MMOPLs (MMF_e and IDMP_e series). Experiments show that NNSL help traditional MMEAs find global PF/PS and local PF/PS simultaneously.