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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.

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.

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.

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.

The purpose of this paper is to focus on the implementation and management of multi‐objective optimizations, with the help of heuristic algorithms such as space mapping methods.

The authors consider the design of electromechanical actuators by the use of mathematical and computer means. Experiments are then virtual, because they correspond to numerical simulations. Dimensioning is then ensured by an optimization procedure of the space mapping type, whose main characteristic consists in using two models of the same size actuator (instead of a single one for classical optimization methods). Moreover, one considers here that multiple outputs are defined: this defines a multi‐objective optimization. This paper proposes several techniques making it possible to include the definition of multiple objectives to be fulfilled as part of an output space mapping optimization process.

The proposed approaches make it possible to stabilize and accelerate the convergence of multi‐objective optimizations performed by space mapping. This is illustrated by the example of the dimensioning of a resonant linear electromagnetic actuator.

The approach presented in the paper is original because it allows finding of a solution to the multi‐objective problem, without building any Pareto front, and most effectively by improving the convergent behavior of the optimization algorithm.

This paper aims to investigate three low-evaluation-budget optimization techniques: output space mapping (OSM), manifold mapping (MM) and Kriging-OSM. Kriging-OSM is an original approach having high-order mapping.

The electromagnetic device to be optimally sized is a five-phase linear induction motor, represented through two levels of modeling: coarse (Kriging model) and fine.The optimization comparison of the three techniques on the five-phase linear induction motor is discussed.

The optimization results show that the OSM takes more time and iteration to converge the optimal solution compared to MM and Kriging-OSM. This is mainly because of the poor quality of the initial Kriging model. In the case of a high-quality coarse model, the OSM technique would show its domination over the other two techniques. In the case of poor quality of coarse model, MM and Kriging-OSM techniques are more efficient to converge to the accurate optimum.

Kriging-OSM is an original approach having high-order mapping. An advantage of this new technique consists in its capability of providing a sufficiently accurate model for each objective and constraint function and makes the coarse model converge toward the fine model more effectively.