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The purpose of this paper is to focus on multiobjective optimization methods that are suitable for industrial electromagnetic design. In particular, a multiobjective optimization procedure is proposed, where the computation time is reduced by adjusting the refinement of the mesh, according to the accuracy required for the search in the design space rather than for the field analysis. A case study, dealing with the shape design of a small generator for automotive applications, is solved by comparing different procedures of optimization. Finally, a review of open problems is presented and discussed.