Multi-objective optimizations by means of 3D finite element models result in very high computation burden. To have an affordable computation cost, the output space-mapping technique is applied with a new method where the scalar correction of the model outputs is replaced by a set of corrective functions. This method is used for the bi-objective optimization of a transformer and allows finding the complete Pareto optimal set in less than two days on a laptop.

Two analytical models and two finite element models (2D and 3D) are built and compared in terms of accuracy and computation time. They can be used as a benchmark to compare algorithms for multi-level and combinatorial optimizations. The discrete optimization of the transformer is done using branch and bound methods. The multi-level optimization is performed using one analytical model and the 3D FE model jointly thanks to the space-mapping techniques.

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