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We present two new strategies for sequential optimization method (SOM) to deal with the optimization design problems of electromagnetic devices. One is a new space reduction strategy; the other is model selection strategy. Meanwhile, radial basis function (RBF) and compactly supported RBF models are investigated to extend the applied model types for SOM. Thereafter, Monte Carlo method is employed to demonstrate the efficiency and superiority of the new space reduction strategy. Five commonly used approximate models are considered for the discussion of model selection strategy. Furthermore, by two TEAM benchmark examples, we can see that SOM with the proposed new strategies and models can significantly speed the optimization design process, and the efficiency of SOM depends a little on the types of approximate models.