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The numerical optimization of continuous parameters in electrotechnical design using electromagnetic field simulation is already standard. When integer-valued variables are involved, the complexity of the optimization problem rises drastically. In this paper, we describe a new sequential surrogate optimization approach for simulation-based mixed-integer nonlinear programming (NLP) problems. We apply the method for the optimization of combined integer- and real-valued geometrical parameters of the coils of a superconductive magnet.