A Bi-Objective Evolutionary Algorithm for Multimodal Multiobjective Optimization
提出一种双目标进化算法，将多模态多目标优化问题转化为双目标优化，通过惩罚边界交叉和多样性指标同时优化收敛性和决策空间多样性，在34个测试问题及6个特征选择问题上优于现有方法。
Multimodal multiobjective optimization problems (MMOPs) possess multiple Pareto optimal sets (PSs) corresponding to the identical Pareto optimal front (PF). To handle MMOPs, we propose a bi-objective evolutionary algorithm (BOEA), which transforms an MMOP into a bi-objective optimization problem. This problem is constructed by the penalty boundary intersection technique and a diversity indicator to obtain multiple PSs. The first objective reflects the population convergence and factors in the population diversity in the objective space, while the other objective concentrates more on the population diversity in the decision space. Furthermore, an environmental selection strategy is designed to choose the offspring solutions, which consists of nondominated sorting based on the transformed optimization problem and hierarchical clustering for selecting promising solutions. Experiments on 34 MMOPs demonstrate that BOEA performs better than selected state-of-the-art representatives, including 22 MMOPs from CEC2019 and 12 imbalanced MMOPs. In addition, the effectiveness of BOEA is further validated by six feature selection problems in real-world applications.