This paper presents a hybrid approach to optimize the counterweight balancing of a robot arm. A new technique that combines an artificial intelligence technique called the genetic algorithm (GA) and the weighted min-max multiobjective optimization method is proposed. These techniques are included in a system developed by the authors, called MOSES, which is intended to be used as a tool for engineering design optimization. The results presented here show how the new proposed technique can get better trade-off solutions and a more accurate Pareto front for this highly non-convex problem using an ad-hoc floating point representation and traditional genetic operators. Finally, a methodology to compute the ideal vector using a genetic algorithm is presented. It is shown how with a very simple dynamic approach to adjust the parameters of the GA, it is possible to obtain better results than those previously reported in the literature for this problem.