This paper presents a rotor shape multi-level-objective optimization designed to reduce the mechanical stress distribution in the rotor core of a double-stator permanent magnet synchronous motor. The second objective is weight minimization performed via a response surface methodology with a uniform precision central composite design function. The optimal operation point, with a substantial population size, is reached using a Monte Carlo algorithm on the fitted model. The goodness-of-fit for the model is evaluated based on the modified Akaike information criterion and the Bayesian information criterion with a linear regression approach. To achieve these goals, a multi-level design procedure is proposed for the first time in machine design engineering. All the electromagnetic forces of the machine, such as normal, tangential, and centrifugal forces, are calculated using three-dimensional transient finite element analysis. The outcome of the proposed rotor core optimization shows that the finalized shape of the studied core has significantly smaller weight and mechanical stress, while the electromagnetic performance of the machine has remained consistent with a pre-optimized machine.