A dynamic-speciation-based differential evolution with ring topology for constrained multimodal multi-objective optimization

Constrained multimodal multi-objective optimization problems (CMMOPs) consist of multiple equivalent constrained Pareto sets (CPSs) that have the identical constrained Pareto front (CPF). It is challenging for primary multimodal multi-objective evolutionary algorithms (MMEAs) to solve CMMOPs since they do not consider constraints. To tackle this challenge, a dynamic speciation-based differential evolution with ring topology, termed DSRDE, for solving CMMOPs is developed in this paper. To search for multiple equivalent CPSs in CMMOPs, the dynamic speciation-based niche strategy is developed. The dynamic speciation-based niche strategy divides the population into multiple species, each of which searches for diverse and equivalent CPSs in different regions. Particularly, the species number is dynamically decreased to explore the equivalent CPSs with good convergence. Then, a ring topology is constructed among multiple species and their neighbors to balance the diversity, convergence, and feasibility of solutions. Continuously, each species interacts information with its neighbors and searches for equivalent CPSs. DSRDE adopts the popular constrained dominance principle to handle constraints and uses the differential evolutionary algorithm to locate diverse CPSs in the ring topology. It is compared with several state-of-the-art algorithms in two CMMOPs test suites for evaluating the performance of the proposed DSRDE. The experimental results confirm that DSRDE is competitive and has the ability to find multiple CPSs when tackling CMMOPs. DSRDE is also implemented in a real-world CMMOP and obtains superior performance.