Performance Evaluation of Evolutionary Multi-Objective Algorithms Using Real-World Problems with an Additional Total Constraint Violation Objective

Yang Nan, Hisao Ishibuchi, Tianye Shu

Abstract: In the community of evolutionary multi-objective optimization (EMO), one important issue is the choice of test problems for performance evaluations of EMO algorithms. This is because performance evaluation results of EMO algorithms totally depend on the choice of test problems. This means that the research on new EMO algorithm design is also influenced by the choice of test problems. Recently, researchers have started to use real-world problems for performance evaluation of EMO algorithms. Among them, a real-world problem suite RE has attracted much attention and has been used in many studies. However, most RE problems have been created from real-world constrained problems by using the total constraint violation as an additional objective. That is, the original versions of most RE problems are not unconstrained multi-objective problems. Thus, even when a good solution set is obtained by an EMO algorithm for an RE problem, it can be a poor solution set for its original constrained problem. This is because many well-distributed solutions over the entire Pareto front of the transformed unconstrained problem are usually infeasible solutions of the original constrained problem with some positive total constraint violation values. In this paper, we examine whether good solution sets obtained by EMO algorithms for RE problems are also good solution sets for their original constrained problems. Our experimental results show that good solutions sets for most RE problems include good feasible solution sets for their original constrained problems. However, for a few RE problems, good solution sets obtained by some high performance EMO algorithms do not include good feasible solution sets. Our results show that high-performance EMO algorithms on most RE problems generate good feasible solution sets for their original constrained versions. This observation supports the usefulness of those RE problems as test problems for performance evaluation of EMO algorithms.