This paper presents an analytical method for improving the optimal design of electromagnetic devices obtained analytically. This method extracts the significant parameters by using the gradient of difference between the outputs of the analytical model and those obtained with a finite-element method. These parameters are then employed to build a response surface in a reduced dimension space by using the moving least square method. To assess its viability, we compared our method to another recent approach in the optimal design of a permanent-magnet synchronous motor. The results show our method's superiority in terms of improvement of the solution and approximation of the real objective function .