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.

在本文中，我们提出了一种具有自适应选择的多阶段进化框架（MSEFAS），用于有效处理约束多目标优化问题（CMOP）。 MSEFAS在进化搜索的早期阶段有两个优化阶段：一个阶段鼓励有希望的不可行解接近可行区域并增加多样性，另一个阶段使种群能够跨越大的不可行区域并加速收敛。为了在流程早期自适应地确定这两个阶段的执行顺序，MSEFAS 将所选解决方案有效性较高的优化阶段视为第一阶段，将其他阶段视为第二阶段。此外，在进化搜索的后期，MSEFAS引入了第三阶段，通过考虑受约束Pareto前沿（CPF）和无约束Pareto前沿之间的关系来有效处理CMOP的各种特征。我们将所提出的框架与 56 个基准 CMOP 上的 11 种最先进的约束多目标进化算法进行了比较。我们的结果证明了所提出的框架在处理各种 CMOP 方面的有效性，展示了其解决复杂优化问题的潜力。