This paper presents an original methodology for machine design. The methodology is based on nonlinear reluctance network modeling and multilevel surrogate based optimization. The reluctance network is solved by computing the meshes magnetic flux and its topology is updated for each rotor position. In order to achieve an optimal design, in terms of satisfying some specifications, a surrogate based optimization inspired from the Space Mapping (SM) technique is considered. Optimization is held on the linear model and is iteratively corrected, through a new embedded strategy, by the nonlinear one. Finally, the proposed application is a constrained minimization of axial flux machine losses on an artemis cycles.