Characterization of Constrained Continuous Multiobjective Optimization Problems: A Performance Space Perspective

Abstract

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 article takes a step toward addressing 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 at simultaneously measuring the performance in approximating the Pareto front and constraint satisfaction. Second, it proposes an approach to measure the capability of the given optimization problem to differentiate among algorithm performances. Finally, this approach is used to compare eight frequently used artificial test suites of CMOPs. The experimental results reveal which suites are more efficient in discerning between four well-known multiobjective optimization algorithms.