A multimodal multi-objective differential evolution with series-parallel combination and dynamic neighbor strategy

Multimodal multi-objective optimization problems (MMOPs), which aim to identify as many optimal solutions as possible and exhibit multiple equivalent Pareto optimal solution sets (PSs) that correspond to the same Pareto optimal front (PF), commonly arise in a wide range of optimization problems in the real world. However, some dominated solutions that exhibit greater diversity in the decision space may be substituted by non-dominated solutions with a higher level of decision space crowding. To tackle this issue, this paper proposes a multimodal multi- objective differential evolution with series-parallel combination and dynamic neighbor strategy (MMODE_SPDN), which can balance convergence, objective space diversity and decision space diversity. Specifically, two archives are initially updated serially followed by the overall update of the parallel structure, in which the serial-first approach can enhance population diversity and the parallel structure can greatly reduce the amount of calculation. In addition, a dynamic neighbor strategy which utilizes adaptive selection among neighbors to generate difference vectors in the decision space and objective space and then adopts the main and auxiliary parent method during the mutation process is proposed. Furthermore, the utilization of an auxiliary archive and the clustering-based special crowding distance (CSCD) method are employed to facilitate the updating of the archive, thereby enhancing diversity. MMODE_SPDN is compared with other multimodal multi-objective optimization evolutionary algorithms (MMOEAs) on numerous test problems and the experimental results demonstrate that MMODE_SPDN exhibits superior performance.