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We present two new sequential optimization strategies, a sequential subspace optimization method (SSOM) and an improved sequential optimization method (SOM) with orthogonal experimental design technique, to deal with optimization design problems of electromagnetic devices in this work. To implement the proposed methods, we first divide the whole design factors into three sets, namely highly-significant, significant, and nonsignificant factors. Then the whole design space can be correspondingly divided into three subspaces with these three sets of factors. Thereafter, SSOM is presented to sequentially optimize those subspaces. In the subspace, we present an improved SOM based on orthogonal experimental design technique to get optimal solutions. Finally, by investigating TEAM benchmark problem 22, we can see that the sampling efficiency can be improved significantly and the computational cost of finite element analysis can be saved remarkably by the proposed methods.