This paper presents a new methodology of design of electrical rotating machines. The methodology is an extension of previous works of the second author. Indeed, associating combinatorial analytical models with exact global optimization algorithms leads to rational solutions of predesign. These solutions need to be validated by a numerical tool (using a finite-element method) before the expansive phase of hand-making a prototype. Such an automatic numerical tool for computing some characteristic values, such as the torque, was previously developed. The idea of this paper is to extend the exact global optimization algorithm by inserting the direct use of this automatic numerical tool. This new methodology makes it possible to solve design problems more rationally. Some numerical examples validate the usefulness of this new approach.