Characterization of Constrained Continuous Multiobjective Optimization Problems: A Feature Space Perspective
This work addresses the difficulty in selecting appropriate CMOPs for benchmarking, which is a problem for researchers and benchmark designers in optimization, though it is incremental as it builds on existing landscape analysis techniques.
The authors tackled the problem of insufficient characterization of constrained multiobjective optimization problems (CMOPs) by extending landscape analysis to propose 29 features, including 19 novel ones, and found that artificial test suites fail to represent realistic characteristics like strong negative correlations between objectives and constraints.
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.