A subspace strategy based coevolutionary framework for constrained multimodal multiobjective optimization problems

Constrained multimodal multiobjective optimization problems (CMMOPs) consist of multiple equivalent constrained Pareto sets (CPSs) that have the identical constrained Pareto front (CPF). The key to solving CMMOPs lies in how to locate and retain CPSs and CPF in search spaces. Thus, this paper proposes a subspace strategy based coevolutionary framework for CMMOPs, named SCCMMO. Firstly, the subspace generation and maintenance strategy is proposed to efficiently locate multiple CPSs within the decision space. Secondly, the subspace-type perception strategy is used to exploit the feasible and infeasible information in subspaces. Finally, a coevolutionary framework is introduced to improve search efficiency. To prove the effectiveness of the algorithm, the proposed method is compared with ten state-of-the-art algorithms on seventeen benchmarks. The results demonstrate the superiority of SCCMMO in solving CMMOPs. Moreover, SCCMMO also achieves better performance on the real-world problem.