In this paper, we propose a first version of a multi-objective evolutionary algorithm that incorporates some coevolutionary concepts. The primary design goal of the proposed approach is to reduce the total number of objective function evaluations required to produce a reasonably good approximation of the true Pareto front of a problem. The main idea of the proposed approach is to concentrate the search effort on promising regions that arise during the evolutionary process as a byproduct of a mechanism that subdivides decision variable space based on an estimate of the relative importance of each decision variable. The proposed approach is validated using several test functions taken from the specialized literature and it is compared with respect to three approaches that are representative of the state-of-the-art in evolutionary multiobjective optimization.