Characterization of constrained continuous multiobjective optimization problems: A feature space perspective

Despite the increasing interest in constrained multiobjective optimization in recent years, constrained multiobjective optimization problems (CMOPs) are still insufficiently understood and characterized. For this reason, the selection of appropriate CMOPs for bench marking 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 the overall constraint violation. Moreover, our findings show that all the studied artificial test suites have advantages and limitations, and that no perfect suite exists. Additionally, the effectiveness of the proposed features at predicting algorithm performance is demonstrated for two multiobjective optimization algorithms. Benchmark designers can use the obtained results to select or generate appropriate CMOP instances based on the characteristics they want to explore.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This article extends landscape analysis to constrained multiobjective optimization and proposes a method for characterizing CMOPs. The method is used to compare artificial test suites and real-world problem suites, revealing the limitations of artificial test problems in representing realistic characteristics. The effectiveness of the proposed features in predicting algorithm performance is demonstrated.