A Diversity-Enhanced Subset Selection Framework for Multimodal Multiobjective Optimization
针对多模态多目标优化问题中决策空间多样性不足的问题，提出一个子集选择框架，能从所有解中选出在目标空间和决策空间都多样性好的子集，提升现有算法的性能。
Multimodality is commonly seen in real-world multiobjective optimization problems (MOPs). In such optimization problems, namely, multimodal MOPs (MMOPs), multiple decision vectors can be projected to the same solution in the objective space (i.e., there are multiple implementations corresponding to that solution). Therefore, the diversity in the decision space is very important for the decision maker when tackling MMOPs. Subset selection methods have been widely used in the field of evolutionary multiobjective optimization for selecting well-distributed solutions (in the objective space) to be presented to the decision maker. However, since most subset selection methods do not consider the diversity of solutions in the decision space, they are not suitable for MMOPs. In this article, we aim to clearly demonstrate the usefulness of subset selection for multimodal multiobjective optimization. We propose a novel subset selection framework that can be easily integrated into existing multimodal multiobjective optimization algorithms. By selecting a prespecified number of solutions with good diversity in both the objective and decision spaces from all the examined solutions, the proposed framework significantly improves the performance of state-of-the-art multimodal multiobjective optimization algorithms on various test problems.