A grid self-adaptive exploration-based algorithm for multimodal multiobjective optimization

Abstract

In multimodal multiobjective optimization, the key is to find as many equivalent Pareto optimal solutions as possible through broad exploration in the decision space. The grid search strategy can achieve quick convergence by guiding the evolution with historical information in each grid while enabling broad exploration. However, inaccurate utilization of information in grids may lead to losing numerous potential solutions, especially on imbalanced problems. In order to resolve this issue, a grid self-adaptive exploration-based algorithm (GSEA) is proposed in this paper. In GSEA, the historical information in the grid is accurately utilized through grid-based self-adaptive exploration and niche clearing methods, which retain a large number of solutions with potential and effectively handle multimodal multiobjective optimization problems (MMOPs). Experimental results show that the proposed algorithm outperforms seven other state-of-the-art multimodal multiobjective evolutionary algorithms (MMEAs) on two types of MMOPs, and the approach can effectively deal with the MMOPs with middle-scale decision variables as memory allows.