A Framework to Handle Multimodal Multiobjective Optimization in Decomposition-Based Evolutionary Algorithms

Multimodal multiobjective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. While decomposition-based evolutionary algorithms have good performance for multiobjective optimization, they are likely to perform poorly for multimodal multiobjective optimization due to the lack of mechanisms to maintain the solution space diversity. To address this issue, this article proposes a framework to improve the performance of decomposition-based evolutionary algorithms for multimodal multiobjective optimization. Our framework is based on three operations: 1) assignment; 2) deletion; and 3) addition operations. One or more individuals can be assigned to the same subproblem to handle multiple equivalent solutions. In each iteration, a child is assigned to a subproblem based on its objective vector, i.e., its location in the objective space. The child is compared with its neighbors in the solution space assigned to the same subproblem. The performance of improved versions of six decomposition-based evolutionary algorithms by our framework is evaluated on various test problems regarding the number of objectives, decision variables, and equivalent Pareto optimal solution sets. Results show that the improved versions perform clearly better than their original algorithms.