A dynamic-ranking-assisted co-evolutionary algorithm for constrained multimodal multi-objective optimization

Constrained multimodal multi-objective optimization problems (CMMOPs) are characterized by multiple constrained Pareto sets (CPSs) sharing the same constrained Pareto front (CPF). The challenge lies in efficiently identifying equivalent CPSs while maintaining a balance among convergence, diversity, and constraints. Addressing this challenge, we propose a dynamic-ranking-based constraint handling technique implemented in a co-evolutionary algorithm, named DRCEA, specifically designed for solving CMMOPs. To search for equivalent CPSs, we introduce a co-evolutionary framework involving two populations: a convergence-first population and a constraint-first population. The co-evolutionary framework facilitates knowledge transfer and sustains diverse solutions. Subsequently, a dynamic ranking strategy is employed with dynamic weight parameters that consider both dominance and constraint relationships among individuals. Within the convergence-first population, the weight parameter for convergence gradually decreases, while the constraint parameter increases. Conversely, in the constraint-first population, the weight parameter for constraints gradually decreases, while the convergence parameter increases. This approach ensures a well-balanced consideration of convergence and constraints within the two distinct populations. Experimental results on the CMMOP test suite and the real-world CMMOP test scenario validate the effectiveness of the proposed dynamic-ranking-based constraint handling technique, demonstrating the superiority of DRCEA over seven state-of-the-art algorithms.