In this paper, we present a technique that uses a combination of the genetic algorithm (GA) and the global criterion method to find the optimum, in the min-max sense, of a multiobjective optimization design problem with multiple constraints. The objectives may be conflicting and noncommensurable, and the technique can deal with minimization and maximization problems (or a mixture of both). The optimum, in the min-max sense, gives a solution that treats all the objectives on terms of equal importance, and presents the advantage of being very efficient and easy to implement. Furthermore, when the min-max approach is combined with the weighting method, we can generate the set of Pareto (nondominant) solutions for both convex and nonconvex problems. Taking advantage of the floating point representation used for the GA, we could solve design problems that involve a mix of continuous, discrete and integer design variables. This technique was tested with multiobjective engineering design problems found in the literature, and our results were compared with traditional mathematical programming techniques that use other search strategies.