In this paper, we propose a new selection mechanism based on epsilon-dominance which is called "epsilon-selection". An interesting feature of this selection scheme is that it does not require to set the value of o ahead of time. Our epsilon-selection is incorporated into the GD-MOEA algorithm, giving rise to the so-called "Generational Distance & epsilon-dominance Multi-Objective Evolutionary Algorithm (GDE-MOEA)". Our proposed GDE-MOEA is validated using standard test functions taken from the specialized literature, having three to six objective functions. GDE-MOEA is compared with respect to the original GD-MOEA, which is based on the generational distance indicator and a technique based on Euclidean distances to improve the diversity in the population. Additionally, our proposed approach is compared with respect to MOEA/D using Penalty Boundary Intersection (PBI), which is based on decomposition, and SMS-EMOA-HYPE ( a version of SMS-EMOA that uses a fitness assignment scheme based on the use of an approximation of the hypervolume indicator). Our preliminary results indicate that our proposed GDE-MOEA is a good alternative to solve multi-objective optimization problems having both low dimensionality and high dimensionality in objective function space because it obtains better results than GD-MOEA and MOEA/D in most cases and it is competitive with respect to SMS-EMOA-HYPE but at a much lower computational cost.