Multi-stage Global and Local Cooperative Constrained Multi-objective Evolutionary Algorithm

When solving constrained multi-objective optimization problems (CMOPs), the primary challenge is to quickly search for the true Pareto fronts (PFs) while ensuring diversity. However, some constrained multi-objective evolutionary algorithms (CMOEAs) employ a single search strategy, making it difficult for their populations to maintain convergence, diversity, and feasibility simultaneously. To address this issue, we propose a novel multi-stage global and local collaborative CMOEA named MSGLC, which includes two different search stages. In the first stage, constraints are ignored, and a CMOP is decomposed into multiple single-objective sub-problems without considering any constraints, allowing the population to quickly search the boundaries of unconstrained PFs, thus improving convergence. In the second stage, through weak co-evolution of the main and auxiliary populations, the main population considers the original CMOP, while the auxiliary population considers the ε-relaxed CMOP. They respectively adopt local and global differential evolution operators for offspring generation. This can help the populations effectively get across multiple large infeasible areas and quickly search for the constrained PF. Furthermore, we introduce a computational resource allocation strategy based on sub-regions, concentrating computational resources in potentially search areas, thereby enhancing the search efficiency of the proposed algorithm. Comparative experimental results demonstrate that the proposed MSGLC significantly outperforms five other state-of-the-art CMOEAs on the LIRCMOP benchmark problems.