Despite the increasing interest in constrained multiobjective optimization in recent years, constrained multiobjective optimization problems (CMOPs) are still unsatisfactory understood and characterized. For this reason, the selection of appropriate CMOPs for benchmarking is difficult and lacks a formal background. We address this issue by extending landscape analysis to constrained multiobjective optimization. By employing four exploratory landscape analysis techniques, we propose 29 landscape features (of which 19 are novel) to characterize CMOPs. These landscape features are then used to compare eight frequently used artificial test suites against a recently proposed suite consisting of real-world problems based on physical models. The experimental results reveal that the artificial test problems fail to adequately represent some realistic characteristics, such as strong negative correlation between the objectives and constraints. Moreover, our findings show that all the studied artificial test suites have advantages and limitations, and that no "perfect" suite exists. Benchmark designers can use the obtained results to select or generate appropriate CMOP instances based on the characteristics they want to explore.
翻译:尽管近年来对限制的多目标优化越来越感兴趣,但受限制的多目标优化问题仍然不能令人满意地理解和定性。因此,为基准选择适当的CPOP问题十分困难,而且缺乏正式背景。我们通过将景观分析扩大到受限制的多目标优化来解决这个问题。我们建议使用四种探索性景观分析技术来描述CMO的特征(其中19种是新奇的 ) 。这些景观特征被用来比较8个经常使用的人工测试套件和最近提出的由基于物理模型的现实世界问题组成的套件。实验结果显示,人工测试问题未能充分代表一些现实的特征,例如目标和制约因素之间的强烈负相关关系。此外,我们的调查结果显示,所有研究过的人工测试套件都具有优势和局限性,不存在“完美”套件。基准设计者可以使用所获得的结果来选择或产生基于他们想要探索的特征的CPMO适当实例。