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Conceiving electromagnetic devices using finite element modeling tools is a complex task and also time-costly. The Efficient Global Optimization method, based on the progressive construction of surrogate models, is studied. The method uses Kriging models and allows for multiobjective optimization. An original infill criterion, combining the surrogate models and an estimate of their error is proposed. Moreover, two techniques for the calculi distribution, adapted to the algorithm, are tested on an eight-core machine. An advantage of the method consists in its capability of providing sufficiently accurate models for each objective and constraint function around the obtained Pareto front. The SMES device of the TEAM problem 22 is used as benchmark.