Despite the successful application of an extension of the Multi-Objective Evolution Algorithm based on Decomposition (MOEA/D-M2M) to solve unbalanced multi-objective optimization problems (UMOPs), its use in constrained unbalanced multi-objective optimization problems has not been fully explored. In an earlier paper, a definition of UMOPs was suggested that had two necessary conditions: 1) finding a favored subset of the Pareto set is easier than finding an unfavored subset, and 2) the favored subset of the Pareto set dominates a large part of the feasible space. The second condition strongly reduces the fraction of MOPs that are considered UMOPs. In this paper, we eliminate that second condition and consider a broader class of UMOPs. We design an unbalanced constrained multi-objective test suite with three different types of biased constraints, yielding three different types of constrained test problems in which the degree of imbalance is scalable via a set of parameters introduced for each problem. We analyse the characteristics of three types of constraints and the difficulties they present for potential solution algorithms–i.e., NSGA-II, MOEA/D and MOEA/D-M2M, with four constraint-handling techniques. MOEA/D-M2M is shown to significantly outperform the other algorithms on these problems due to its decomposition strategy.

尽管成功地应用了基于分解的多目标进化算法（MOEA / D-M2M）的扩展来解决不平衡的多目标优化问题（UMOP），但其在约束条件下的使用不平衡的多目标优化问题尚未得到充分探讨。在较早的论文中，有人提出了UMOP的定义，该定义具有两个必要条件：1）找到Pareto集的偏爱子集比找到不利集更容易，并且2）Pareto集的偏爱子集占大部分。可行的空间。第二个条件大大降低了被认为是UMOP的MOP的比例。在本文中，我们消除了第二个条件，并考虑了更广泛的UMOP类。我们设计了一种具有三种不同类型的有偏约束的不平衡约束多目标测试套件，产生了三种不同类型的约束测试问题，其中不平衡的程度可以通过针对每个问题引入的一组参数进行扩展。我们使用三种约束处理技术分析了三种约束类型的特征以及它们对于潜在求解算法（即NSGA-II，MOEA / D和MOEA / D-M2M）所带来的困难。由于其分解策略，在这些问题上，MOEA / D-M2M表现出明显优于其他算法。