A constrained multimodal multi-objective evolutionary algorithm based on adaptive epsilon method and two-level selection

Constrained multimodal multi-objective optimization problems (CMMOPs) commonly arise in practical problems in which multiple Pareto optimal sets (POSs) correspond to one Pareto optimal front (POF). The existence of constraints and multimodal characteristics makes it challenging to design effective algorithms that promote diversity in the decision space and convergence in the objective space. Therefore, this paper proposes a novel constrained multimodal multi-objective evolutionary algorithm, namely CM-MOEA, to address CMMOPs. In CM-MOEA, an adaptive epsilon-constrained method is designed to utilize promising infeasible solutions, promoting exploration in the search space. Then, a diversity-based offspring generation method is performed to select diverse solutions for mutation, searching for more equivalent POSs. Furthermore, the two-level environmental selection strategy that combines local and global environmental selection is developed to guarantee diversity and convergence of solutions. Finally, we design an archive update strategy that stores well-distributed excellent solutions, which more effectively approach the true POF. The proposed CM-MOEA is compared with several state-of-the-art algorithms on 17 test problems. The experimental results demonstrate that the proposed CM-MOEA has significant advantages in solving CMMOPs.