Combining Convergence and Diversity in Evolutionary Multiobjective Optimization

TLDR

Evolutionary algorithms are widely used for multiobjective optimization to find Pareto‑optimal solutions, yet existing methods lack a proof of convergence while maintaining diverse solutions. This paper examines why earlier MOEAs fail to achieve both convergence and diversity. The authors introduce ɛ‑dominance–based archiving strategies and additional algorithmic modifications that guarantee convergence to the true Pareto set while preserving solution diversity. The ɛ‑dominance approach proves effective, rendering the resulting algorithms valuable for both research and practical applications.

Abstract

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective 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 Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective 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. Based on the concept of ɛ-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of ɛ-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.