Constrained multi-objective optimization problems (CMOPs) are challenging because of the difficulty in handling both multiple objectives and constraints. While some evolutionary algorithms have demonstrated high performance on most CMOPs, they exhibit bad convergence or diversity performance on CMOPs with small feasible regions. To remedy this issue, this paper proposes a coevolutionary framework for constrained multi-objective optimization, which solves a complex CMOP assisted by a simple helper problem. The proposed framework evolves one population to solve the original CMOP and evolves another population to solve a helper problem derived from the original one. While the two populations are evolved by the same optimizer separately, the assistance in solving the original CMOP is achieved by sharing useful information between the two populations. In the experiments, the proposed framework is compared to several state-of-the-art algorithms tailored for CMOPs. High competitiveness of the proposed framework is demonstrated by applying it to 47 benchmark CMOPs and the vehicle routing problem with time windows.

中文翻译：

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约束多目标优化问题的协同进化框架

由于难以同时处理多个目标和约束，约束多目标优化问题 (CMOP) 具有挑战性。虽然一些进化算法在大多数 CMOP 上表现出高性能，但它们在具有小可行区域的 CMOP 上表现出较差的收敛性或多样性性能。为了解决这个问题，本文提出了一种用于约束多目标优化的协同进化框架，该框架解决了由简单辅助问题辅助的复杂 CMOP。所提出的框架进化出一个种群来解决原始的 CMOP，并进化出另一个种群来解决从原始种群衍生的辅助问题。虽然这两个种群分别由同一个优化器进化，但通过在两个种群之间共享有用信息来帮助解决原始 CMOP。在实验中，将所提出的框架与为 CMOP 量身定制的几种最先进的算法进行了比较。通过将其应用于 47 个基准 CMOP 和具有时间窗口的车辆路径问题，证明了所提出框架的高竞争力。