On the Convergence and Diversity-Preservation Properties of Multi-Objective Evolutionary Algorithms

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 Paretooptimal 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 ǫ-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.