Purpose This paper aims to introduce an original application of the corrected response surface method (CRSM) in the context of the optimal design of a permanent magnet synchronous machine used as an integrated starter generator. This method makes it possible to carry out this design in a very efficient manner, in comparison with conventional optimization approaches. Design/methodology/approach The search for optimal conditions is achieved by the joint use of two multi-physics models of the machine to be optimized. The former models most finely the physical functioning of the machine; it is called “fine model”. The second model describes the same physical phenomena as the fine model but must be much quicker to evaluate. Thus, to minimize its evaluation time, it is necessary to simplify it considerably. It is called “coarse model”. The lightness of the coarse model allows it to be used intensively by conventional optimization algorithms. On the other hand, the fine reference model makes it possible to recalibrate the results obtained from the coarse model at any instant, and mainly at the end of each classical optimization. The difference in definition between fine and coarse models implies that these two models do not give the same output values for the same input configuration. The approach described in this study proposes to correct the values of the coarse model outputs by constructing an adjustment (correcting) response surface. This gives the name to this method. It then becomes possible to have the entire load of the optimization carried over to the coarse model adjusted by the addition of this correction response surface. Findings The application of this method shows satisfactory results, in particular in comparison with those obtained with a traditional optimization approach based on a single (fine) model. It thus appears that the approach by CRSM makes it possible to converge much more quickly toward the optimal configurations. Also, the use of response surfaces for optimization makes it possible to capitalize the modeling data, thus making it possible to reuse them, if necessary, for subsequent optimal design studies. Numerous tests show that this approach is relatively robust to the variations of many important functioning parameters. Originality/value The CRSM technique is an indirect multi-model optimization method. This paper presents the application of this relatively undeveloped optimization approach, combining the features and benefits of (Indirect) efficient global optimization techniques and (multi-model) space mapping methods.