The cooling process in polymer injection molding is of great importance as it has a direct impact on both productivity and product quality. In this paper a Multi-objective Optimization Genetic Algorithm, denoted as Reduced Pareto Set Genetic Algorithm with Elitism (RPSGAe), was applied to optimize both the position and the layout of the cooling channels in the injection molding process. The optimization model proposed in this paper is an integration of genetic algorithms and Computer-Aided Engineering, CAE, technology applied to polymer process simulations. The main goal is to implement an automatic optimization scheme capable of defining the best position and layout of the cooling channels and/or setting the processing conditions of injection moldings. In this work the methodology is applied to an L-shape molding with the aim of minimizing the part warpage quantified by two different conflicting measures. The results produced have physical meaning and correspond to a successful process optimization.