A multi-stage multi-task evolutionary algorithm for constrained multi-objective optimization

Constraints in constrained multi-objective optimization problems (CMOPs) critically determine the structure of the feasible region and pose significant challenges for optimization. While auxiliary problems have been widely adopted in recent constrained multi-objective evolutionary algorithms (CMOEAs) to enhance constraint-handling capabilities, existing methods typically employ a single auxiliary constraint-handling technique (CHT) within a fixed optimization framework. This limits their ability to handle different types of CMOPs with various constraint features. To address this issue, this paper develops a novel multi-stage multi-task framework that integrates multiple CHTs to enhance the exploration of constrained Pareto front (CPF). The framework employs the constrained dominance principle to guide the evolution of the main population, while an auxiliary population is leveraged to assist in exploring promising feasible regions. It introduces two auxiliary populations: one handling unconstrained problems and the other addressing relaxed constraint problems through the epsilon constraint method. The search process is divided into two stages, employing different task combinations and collaborative methods tailored to meet the evolutionary needs of each stage. Stage 1 explores the unconstrained Pareto front (UPF) and feasible regions, while Stage 2 searches the CPF from both feasible and infeasible regions. Experimental results demonstrate that the proposed framework effectively solves various CMOPs, outperforming or matching ten state-of-the-art methods. This approach provides a comprehensive solution for addressing CMOPs.