An Instance Space Analysis of Constrained Multiobjective Optimization Problems

Abstract

Constrained multi-objective optimization problems (CMOPs) are generally more challenging than unconstrained problems. This in part can be attributed to the infeasible region generated by the constraint functions, the interaction between constraints and objectives, or both. In this paper, we explore the relationship between the performance of constrained multi-objective evolutionary algorithms (CMOEAs) and the instance characteristics of CMOP using Instance Space Analysis (ISA). To do this, we extend recent work on Landscape Analysis features for characterising CMOPs. Specifically, we introduce new features to describe the multi-objective-violation landscape, formed by the interaction between constraint violation and multi-objective fitness. Detailed evaluation of the algorithm footprints, spanning eight CMOP benchmark suites and fifteen CMOEAs, demonstrates that ISA effectively captures the strength and weakness of the CMOEAs. We conclude that two characteristics, the isolation of non-dominate set and the correlation between constraints and objectives evolvability, have the greatest impact on algorithm performance. However, the current benchmarks problems lack of diversity to represent the real-world problems and to fully reveal the efficacy of CMOEAs evaluated.