Evolutionary multi-objective optimization using benson’s karush-kuhn-tucker proximity measure

Abstract

Many Evolutionary Algorithms (EAs) have been proposed over the last decade aiming at solving multi- and many-objective optimization problems. Although EA literature is rich in performance metrics designed specifically to evaluate the convergence ability of these algorithms, most of these metrics require the knowledge of the true Pareto Optimal (PO) front. In this paper, we suggest a novel Karush-Kuhn-Tucker (KKT) based proximity measure using Benson’s method (we call it B-KKTPM). B-KKTPM can determine the relative closeness of any point from the true PO front, without prior knowledge of this front. Finally, we integrate the proposed metric with two recent algorithms and apply it on several multi and many-objective optimization problems. Results show that B-KKTPM can be used as a termination condition for an Evolutionary Multi-objective Optimization (EMO) approach.