A Co-Evolutionary Scheme for Multi-Objective Evolutionary Algorithms Based on $\epsilon$ -Dominance

Convergence and diversity of solutions play an essential role in the design of multi-objective evolutionary algorithms (MOEAs). Among the available diversity mechanisms, the <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-dominance has shown a proper balance between convergence and diversity. When using <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-dominance, diversity is ensured by partitioning the objective space into boxes of size <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> and, typically, a single solution is allowed at each of these boxes. However, there is no easy way to determine the precise value of <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>. In this paper, we investigate how this goal can be achieved by using a co-evolutionary scheme that looks for the proper values of <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> along the search without any need of a previous user’s knowledge. We include the proposed co-evolutionary scheme into an MOEA based on <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-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.

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