Two-Phase Procedure for Efficiently Removing Dominated Solutions From Large Solution Sets

Tianye Shu, Yang Nan, Ke Shang, Hisao Ishibuchi

Abstract: In evolutionary multi-objective optimization (EMO), one important procedure is to remove all dominated solutions from a solution set (e.g., solutions in an archive) to obtain an approximated Pareto front, which is called a static nondominance problem. Recently, an unbounded external archive (UEA) is used in EMO algorithms in many studies to store all solutions examined during the evolutionary process. In these studies, the candidate set in the static nondominance problem includes all the examined solutions. Although many methods have been proposed to solve the static nondominance problem, the dominated solution removal is still time-consuming for a large-scale candidate set. To tackle this issue, we propose a simple and general two-phase procedure to improve the efficiency of existing dominated solution removal methods. In the first phase of our procedure, a large-scale candidate set is divided into several subsets. Dominated solutions are removed from each subset independently, and remaining solutions are merged. In the second phase, dominated solutions are removed from the merged set. Compared with directly removing all dominated solutions from the candidate set, our experimental results show that the proposed two-phase procedure can drastically decrease the computation time when the percentage of nondominated solutions in the candidate set is small.