The balance between proximity and diversity in multiobjective evolutionary algorithms

Over the last decade, a variety of evolutionary algorithms (EAs) have been proposed for solving multi–objective optimization problems. Especially more recent multi–objective evolutionary algorithms (MOEAs) have been shown to be efficient and superior to earlier approaches. In the development of new MOEAs, the strive is to obtain increasingly better performing MOEAs. 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. The best MOEAs to date behave similarly or are individually preferable with respect to different performance indicators. 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 multi–objective problems. While we will point out the most important aspects for designing competent MOEAs in this paper, we will also indicate the inherent multi–objective trade–off in multi–objective optimization between proximity and diversity preservation. We will discuss the impact of this trade–off 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 non–domination selection pressure from diversity preservation selection pressure and discuss the impact of changing the ratio between these components.