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Multiobjective optimization of shielding devices for eddy-currents is studied using several fundamentally different optimization methods. To solve the binary optimization problem of finding an optimal topology of the magnetic shunts a micro-genetic algorithm is used. In order to perform a parameter optimization of a given topology in terms of its placement, evolutionary strategies are applied. Finally, the multiobjective mixed binary-real optimization problem, with respect to both the topology and position of the magnetic shunts, is defined and solved using the micro-genetic algorithm. The conflicting objectives of minimizing Ohmic losses in the shielded body along with minimizing the volume of the shunts' magnetic material are taken into account in two different approaches. On the one hand all objectives are transformed into a single scalar value using the method of weighted functions; on the other hand Pareto optimal solutions are evaluated and assessed. To ensure the reliability of the obtained solutions, the evaluation of the objective functions is based on the 2-D finite-element method eddy-current analysis using both self developed and commercial field solvers.