Here we address the problem of computing the set of approximate solutions of a given multi-objective optimization problem (MOP). This set is of potential interest for the decision maker since it might give him/her additional solutions to the optimal ones for the realization of the project related to the MOP. In this study, we make a first attempt to adapt well-known cell mapping techniques for the global analysis of dynamical systems to the problem at hand. Due to their global approach, these methods are well-suited for the thorough investigation of small problems, including the computation of the set of approximate solutions. We conclude this work with the presentation of three academic bi-objective optimization problems including a comparison to a related evolutionary approach.