The design of an electromagnetic machine is a nonlinear, multivariable, and multimodal optimization problem that incurs a great deal of computation time when calculating electromagnetic fields. To overcome these problems effectively, this paper proposes a new evolutionary multimodal optimization algorithm based on the Big Bang-Big Crunch method and aided by a surrogate model using the theory of compressed sensing. Its efficiency is demonstrated by assessing the optimization results for test functions. Moreover, to evaluate the feasibility of its application to an electromagnetic problem, an interior permanent magnet motor is designed using the proposed algorithm. The obtained results confirm that the proposed method has the ability to search for multiple optimal solutions with a good computational efficiency by reducing the number of fitness function evaluations during the optimization process.