Multiobjective Differential Evolution for Higher-Dimensional Multimodal Multiobjective Optimization

In multimodal multiobjective optimization problems (MMOPs), there are several Pareto optimal solutions corresponding to the identical objective vector. This paper proposes a new differential evolution algorithm to solve MMOPs with higher-dimensional decision variables. Due to the increase in the dimensions of decision variables in real-world MMOPs, it is difficult for current multimodal multiobjective optimization evolutionary algorithms (MMOEAs) to find multiple Pareto optimal solutions. The proposed algorithm adopts a dual-population framework and an improved environmental selection method. It utilizes a convergence archive to help the first population improve the quality of solutions. The improved environmental selection method enables the other population to search the remaining decision space and reserve more Pareto optimal solutions through the information of the first population. The combination of these two strategies helps to effectively balance and enhance convergence and diversity performance. In addition, to study the performance of the proposed algorithm, a novel set of multimodal multiobjective optimization test functions with extensible decision variables is designed. The proposed MMOEA is certified to be effective through comparison with six state-of-the-art MMOEAs on the test functions.