Constrained multiobjective optimization has gained much interest in the past few years. However, constrained multiobjective optimization problems (CMOPs) are still unsatisfactorily understood. Consequently, the choice of adequate CMOPs for benchmarking is difficult and lacks a formal background. This paper addresses this issue by exploring CMOPs from a performance space perspective. First, it presents a novel performance assessment approach designed explicitly for constrained multiobjective optimization. This methodology offers a first attempt to simultaneously measure the performance in approximating the Pareto front and constraint satisfaction. Secondly, it proposes an approach to measure the capability of the given optimization problem to differentiate among algorithm performances. Finally, this approach is used to contrast eight frequently used artificial test suites of CMOPs. The experimental results reveal which suites are more efficient in discerning between three well-known multiobjective optimization algorithms. Benchmark designers can use these results to select the most appropriate CMOPs for their needs.

翻译：约束多目标优化在过去几年中引起了广泛关注。然而，约束多目标优化问题（CMOPs）仍未得到充分理解。因此，选择适当的CMOPs进行基准测试存在困难，且缺乏正式的理论基础。本文通过从性能空间视角探索CMOPs来解决这一问题。首先，提出了一种专门为约束多目标优化设计的新型性能评估方法。该方法首次尝试同时衡量逼近帕累托前沿的性能和约束满足度。其次，提出了一种衡量给定优化问题区分算法性能能力的方法。最后，利用该方法对比了八个常用的人工CMOPs测试集。实验结果表明，哪些测试集能更有效地区分三种知名的多目标优化算法。基准测试设计者可以利用这些结果为自身需求选择最合适的CMOPs。