The main aim of this paper is the imposition of constraints for the multiobjective optimizations of magnetic gears. In order to reduce the computational effort, a semianalytic design procedure is adopted, providing a fast simulation tool that can be embedded within an optimization loop. Magnetic, thermal, and mechanical constraints are discussed and embedded into a stochastic algorithm, in order to identify immediately infeasible geometries. The algorithm that has been developed provides a useful initial design tool that can be adopted to locate the optimal solutions in the search space. This paper also presents the multistage magnetic gear topology as the counterpart of the multistage mechanical gearboxes.