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A novel approach to the three-dimensional optimal design of magnetic shields is presented, in which both shape optimization and topology optimization are achieved with the aid of numerical magnetic-field analysis. These numerical procedures are implemented by means of the hybrid finite element and boundary element method combined with the genetic algorithm. This results in an overall increase in the optimization speed with acceptable computational accuracy. Finally, some numerical results that demonstrate the validity of the proposed approach are presented. © 1997 American Institute of Physics.