The balance between proximity and diversity in multiobjective evolutionary algorithms

TLDR

Over the past decade, numerous evolutionary algorithms have been developed for multiobjective optimization, with recent MOEAs demonstrating superior efficiency compared to earlier approaches. The study questions whether these advances can converge on a single most efficient MOEA, arguing that performance inherently reflects the diverse characteristics of multiobjective problems. The authors analyze the trade‑off between proximity and diversity, examine its influence on exploration and exploitation operators, and propose a general framework that subsumes current state‑of‑the‑art MOEAs through specific design choices. An illustrative example shows how separating nondomination selection pressure from diversity preservation pressure and varying their ratio affects algorithm performance.

Abstract

Over the last decade, a variety of evolutionary algorithms (EAs) have been proposed for solving multiobjective optimization problems. Especially more recent multiobjective evolutionary algorithms (MOEAs) have been shown to be efficient and superior to earlier approaches. An important question however is whether we can expect such improvements to converge onto a specific efficient MOEA that behaves best on a large variety of problems. In this paper, we argue that the development of new MOEAs cannot converge onto a single new most efficient MOEA because the performance of MOEAs shows characteristics of multiobjective problems. While we point out the most important aspects for designing competent MOEAs in this paper, we also indicate the inherent multiobjective tradeoff in multiobjective optimization between proximity and diversity preservation. We discuss the impact of this tradeoff on the concepts and design of exploration and exploitation operators. We also present a general framework for competent MOEAs and show how current state-of-the-art MOEAs can be obtained by making choices within this framework. Furthermore, we show an example of how we can separate nondomination selection pressure from diversity preservation selection pressure and discuss the impact of changing the ratio between these components.