A Co-Evolutionary Scheme for Multi-Objective Evolutionary Algorithms Based on <inline-formula> <tex-math notation="LaTeX">$\epsilon$ </tex-math></inline-formula>-Dominance

Abstract

Convergence and diversity of solutions play an essential role in the design of multi-objective evolutionary algorithms (MOEAs). Among the available diversity mechanisms, the $\epsilon $ -dominance has shown a proper balance between convergence and diversity. When using $\epsilon $ -dominance, diversity is ensured by partitioning the objective space into boxes of size $\epsilon $ and, typically, a single solution is allowed at each of these boxes. However, there is no easy way to determine the precise value of $\epsilon $ . In this paper, we investigate how this goal can be achieved by using a co-evolutionary scheme that looks for the proper values of $\epsilon $ along the search without any need of a previous user’s knowledge. We include the proposed co-evolutionary scheme into an MOEA based on $\epsilon $ -dominance giving rise to a new MOEA. We evaluate the proposed MOEA solving standard benchmark test problems. According to our results, it is a promising alternative for solving multi-objective optimization problems because three main reasons: 1) it is competitive concerning state-of-the-art MOEAs, 2) it does not need extra information about the problem, and 3) it is computationally efficient.

Keywords

• Multi-objective evolutionary algorithms
• ϵ-dominance%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ϵ</italic>-dominance
• co-evolutionary schemes
• parameter setting