In this article, a Hybrid Excitation Synchronous Machine (HESM) is optimally designed for a specified Hybridization Ratio (HR). A new formulation of the design problem is proposed to be tackled by the Non-dominated Sorting Genetic Algorithm II (NSGA-II), while minimizing the material cost. This formulation includes a more comprehensive explanation of the key concept, HR, which considers the soft and hard saturation effects in the HESM design. The HESM model is based on a 3D nonlinear Magnetic Equivalent Circuit (MEC). For faster convergence, the number of design variables is reduced using two statistical analyses, namely Analysis of Level and Analysis of Variance (ANOVA). A HESM is optimally designed for HR = 0.5 and validated by a commercial Finite Element Analysis (FEA) software.