A flexible tri-stage dual-population evolutionary algorithm for constrained multi-objective optimization

Constrained multi-objective optimization problems (CMOPs) have garnered significant attention in recent years, leading to the development of numerous constrained multi-objective evolutionary algorithms (CMOEAs). For certain CMOPs with complex frontier landscapes and small feasible domains, efficiently allocating limited computing resources to accurately identify the constrained Pareto front (CPF) is a significant challenge. To address these challenges, this paper introduces a flexible tri-stage CMOEA designed to optimize the allocation of computational resources. The algorithm consists of three distinct stages: the exploration stage, the cooperation stage, and the convergence stage. Each optimization stage involves offspring generation and environmental selection by distinct populations tailored to the specific goals of that stage. Additionally, the paper proposes two effective stage transition conditions that accurately assess the population’s current state, ensuring a smooth progression through the optimization process. The proposed algorithm was evaluated on 43 instances from four test suites and compared against 11 state-of-the-art CMOEAs. The results demonstrate that TriSEA effectively allocates computing resources, leading to competitive experimental outcomes.