Adaptive multi-stage evolutionary search for constrained multi-objective optimization

In this paper, we propose a multi-stage evolutionary framework with adaptive selection (MSEFAS) for efficiently handling constrained multi-objective optimization problems (CMOPs). MSEFAS has two stages of optimization in its early phase of evolutionary search: one stage that encourages promising infeasible solutions to approach the feasible region and increases diversity, and the other stage that enables the population to span large infeasible regions and accelerates convergence. To adaptively determine the execution order of these two stages in the early process, MSEFAS treats the optimization stage with higher validity of selected solutions as the first stage and the other as the second one. In addition, at the late phase of evolutionary search, MSEFAS introduces a third stage to efficiently handle the various characteristics of CMOPs by considering the relationship between the constrained Pareto fronts (CPF) and unconstrained Pareto fronts. We compare the proposed framework with eleven state-of-the-art constrained multi-objective evolutionary algorithms on 56 benchmark CMOPs. Our results demonstrate the effectiveness of the proposed framework in handling a wide range of CMOPs, showcasing its potential for solving complex optimization problems.