In an electromagnetic machine with permanent magnets the excitation field is provided by a permanent magnet instead of a coil. The center of the generator, the rotor, contains the magnet. Our optimization goal consists in finding the minimum volume of the magnet which gives a desired electromotive force. This is a standard optimization problem with PDE constraints. We propose a goal-oriented model order reduction approach to provide a reduced order surrogate model for the parametrized PDE which then is utilized in the numerical optimization. One important feature of the proposed scheme is the online update of the basis functions which allows to avoid expensive offline stages. Numerical tests will be provided in order to show the effectiveness of the proposed method. Joint work with M. Hinze, O. Lass and S.Ulbrich.