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