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

TL;DR

This paper introduces a new performance assessment method for constrained multiobjective optimization problems, enabling better benchmarking and differentiation of algorithm performance across various test suites.

Contribution

It presents a novel performance evaluation approach for CMOPs and applies it to compare eight common test suites, aiding benchmark design.

Findings

Identifies which test suites better differentiate algorithm performance.

Provides a new metric for assessing constraint satisfaction and Pareto front approximation.

Highlights the importance of test suite selection in benchmarking.

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 paper addresses 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 to simultaneously measure the performance in approximating the Pareto front and constraint satisfaction. Secondly, it proposes an approach to measure the capability of the given optimization problem to differentiate among algorithm performances. Finally, this approach is used to contrast eight frequently used artificial test suites of CMOPs. The experimental results reveal which suites are more efficient in discerning between three well-known multiobjective optimization algorithms. Benchmark designers can use these results to select the most appropriate CMOPs for their needs.