We analyze here some properties of the maximin fitness function, which has been used by several researchers, as an alternative to Pareto optimality, for solving multi-objective optimization problems. As part of this analysis, we identify some disadvantages of the maximin fitness function and then propose mechanisms to overcome them. This leads to several selection operators for multi-objective evolutionary algorithms which are further analyzed. We incorporate them into an evolutionary algorithm, giving rise to the so-called Maximin-Clustering Multi-Objective Evolutionary Algorithm (MC-MOEA) approach. Our proposed approach is validated using standard test problems taken from the specialized literature, having from two to eight objectives. Our preliminary results indicate that our proposed approach is a good alternative to solve multi-objective optimization problems having both low dimensionality (two or three) and high dimensionality (more than three) in objective function space.