Using the Local Auxiliary Population to Balance the Convergence and Constraints in Constrained Multimodal Multi-objective Optimization

Many constrained multimodal multi-objective evolutionary algorithms (CMMEAs) can effectively solve constrained multimodal multi-objective optimization problems (CMMOPs) with multiple equivalent constrained Pareto optimal solution sets (CPSs) mapped to the same constrained Pareto optimal front (CPF). Due to the existence of the constraint-first mechanism, these CMMEAs will delete solutions that can improve convergence of the CPS but violate the constraints to a large extent and even ignore the CPS with high constraint strength when encountering the CPS with the imbalance between convergence and constraints. To solve the above problems, this paper proposes a co-evolutionary algorithm with a local auxiliary population. The main population searches for all equivalent CPSs through the constraint-based global Pareto dominance principle. The local auxiliary population weakens the mutual influence of convergence and diversity between regions with different constraint strengths through the local Pareto dominance principle and provides more solutions around CPSs with higher constraint strengths to the main population. The proposed method is compared with five state-of-the-art CMMEAs on 31 CMMOPs, and the experimental results show that the proposed method is competitive.