In dealing with constrained multi-objective optimization problems (CMOPs), a key issue of multi-objective evolutionary algorithms (MOEAs) is to balance the convergence and diversity of working populations. However, most state-of-the-art MOEAs show poor performance in balancing them, and can cause the working populations to concentrate on part of the Pareto fronts, leading to serious imbalanced searching between preserving diversity and achieving convergence. This paper proposes a method which combines a multi-objective to multi-objective (M2M) decomposition approach with the push and pull search (PPS) framework, namely PPS-M2M. To be more specific, the proposed algorithm decomposes a CMOP into a set of simple CMOPs. Each simple CMOP corresponds to a sub-population and is solved in a collaborative manner. When dealing with constraints, each sub-population follows a procedure of “ignore the constraints in the push stage and consider the constraints in the pull stage”, which helps each working sub-population get across infeasible regions. In order to evaluate the performance of the proposed PPS-M2M, it is compared with the other nine algorithms, including CM2M, MOEA/D-Epsilon, MOEA/D-SR, MOEA/D-CDP, C-MOEA/D, NSGA-II-CDP, MODE-ECHM, CM2M2 and MODE-SaE on a set of benchmark CMOPs. The experimental results show that the proposed PPS-M2M is significantly better than the other nine algorithms. In addition, a set of constrained and imbalanced multi-objective optimization problems (CIMOPs) are suggested to compare PPS-M2M and PPS-MOEA/D. The experimental results show that the proposed PPS-M2M outperforms PPS-MOEA/D on CIMOPs.

在处理受限的多目标优化问题（CMOP）时，多目标进化算法（MOEA）的关键问题是平衡工作人口的收敛性和多样性。但是，大多数最先进的MOEA在平衡它们方面的表现都很差，并且可能导致工作人群专注于Pareto前沿的一部分，从而导致在维护多样性和实现融合之间进行严重的失衡搜索。本文提出了一种将多目标到多目标（M2M）分解方法与推拉搜索（PPS）框架相结合的方法，即PPS-M2M。更具体地说，所提出的算法将CMOP分解为一组简单的CMOP。每个简单的CMOP都对应一个子群体，并以协作方式解决。在处理约束时，每个子种群都遵循“忽略推入阶段的约束并考虑拉动阶段的约束”的过程，这有助于每个工作子种群跨越不可行的区域。为了评估所提出的PPS-M2M的性能，将其与其他9种算法进行了比较，包括CM2M，MOEA / D-Epsilon，MOEA / D-SR，MOEA / D-CDP，C-MOEA / D，NSGA -II-CDP，MODE-ECHM，CM2M2和MODE-SaE基于一组基准CMOP。实验结果表明，提出的PPS-M2M明显优于其他九种算法。此外，建议使用一组受约束和不平衡的多目标优化问题（CIMOP）来比较PPS-M2M和PPS-MOEA / D。实验结果表明，在CIMOP上，拟议的PPS-M2M优于PPS-MOEA / D。