Metal parts produced by additive manufacturing often require postprocessing to meet the specifications of the final product, which can make the process chain long and complex. Laser post-processes can be a valuable addition to conventional finishing methods. Laser polishing, specifically, is proving to be a great asset in improving the surface quality of parts in a relatively short time. For process development, experimental analysis can be extensive and expensive regarding the time requirement and laboratory facilities, while computational simulations demand the development of numerical models that, once validated, provide valuable tools for parameter optimization. In this work, experiments and simulations are performed based on the design of experiments to assess the effects of the parametric inputs on the resulting surface roughness and heat-affected zone depths. The data obtained are used to create both linear regression and artificial neural network models for each variable. The models with the best performance are then used in a multiobjective genetic algorithm optimization to establish combinations of parameters. The proposed approach successfully identifies an acceptable range of values for the given input parameters (laser power, focal offset, axial feed rate, number of repetitions, and scanning speed) to produce satisfactory values of Ra and HAZ simultaneously.