Constrained multimodal multi-objective optimization: Test problem construction and algorithm design

Solving multimodal multi-objective optimization problems (MMOPs) has received increasing attention. How-ever, recent studies only consider unconstrained MMOPs. Given the fact that there are usually constraints in real-world optimization problems, in this work, we propose a test problem construction approach for constrained multimodal multi-objective optimization. Based on the approach, a test suite, containing 14 instances with diverse features and difficulties, is created. Meanwhile, a new evolutionary framework is tailored for this kind of problem. We test the proposed framework in the experiments and compare it to state-of-the-art multimodal multi-objective optimization algorithms on the proposed test suite. The results reveal that the proposed test suite is challenging and it can motivate researchers to develop new algorithms. In addition, the superiority of our proposed framework demonstrates its effectiveness in handling constrained MMOPs.