Multifaceted collaborative evolutionary constrained multimodal multiobjective optimization

In addressing constrained multimodal multiobjective optimization problems (CMMOPs), this paper proposes a multifaceted collaborative evolutionary algorithm (MCEA) designed to balance feasibility, convergence, and diversity in both the objective and decision spaces. Existing approaches often focus solely on maintaining population diversity or feasibility, neglecting the intricacies of CMMOPs, which require simultaneous consideration of multiple conflicting goals. Our MCEA framework features a local–global collaborative search strategy that employs dynamic clustering for effective exploration and exploitation of diverse decision space regions. Additionally, a parent–offspring collaborative transfer strategy facilitates knowledge sharing between populations, enhancing convergence early in the evolutionary process and preserving diversity in later stages. Furthermore, we customize an objective-search space collaborative selection strategy that filters solutions based on population diversity across both spaces. Extensive experiments on thirty-one benchmark CMMOPs demonstrate that MCEA significantly outperforms state-of-the-art algorithms on more than half of the test problems, as measured by IGD, IGDX, RPSP, and HV performance indicators. Furthermore, MCEA effectively locates multiple Pareto subsets, showcasing its ability to balance convergence, diversity, and feasibility in solving CMMOPs. This work underscores the importance of a comprehensive approach to tackling the complexities of CMMOPs and provides valuable insights for future research in this domain.