On the convergence and diversity-preservation properties of multi-objective evolutionary algorithms

Abstract

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multi-objective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the true Pareto-optimal solutions with a widely spread distribution of solutions. However, none of the multi-objective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties and then suggest a class of archive-based MOEAs which can have both properties of converging to the true Pareto-optimal front and maintain a spread among obtained solutions. A number of modifications to the baseline algorithm are also suggested. The concept of epsilon dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.