For accurate modeling of electrical machines the solution multiple physical fields simultaneously in 3D is necessary. Therefore, the optimization of these machines is an computationally expensive optimization problem. The novel artificial intelligence methods and surrogate modeling techniques based on hp-adaptive FEM techniques can significantly reduce the computational cost. In case of a cogging torque or a torque ripple calculation, many simulations should be performed to make an accurate estimation of a single quantity. The number of calculations can be reduced by using surrogate modeling techniques. However, the surrogate model-based model's extrema can differ from the original task's optima. This paper presents a surrogate-model based cogging torque minimization of an axial flux permanent magnet synchronous machine. The objective function of this optimization is the cogging torque, the full solution space is explored to examine and show the robustness of the different kind of solutions.