Improved sequential optimization method (SOM) and dimension reduction optimization method (DROM) are presented for high dimensional optimization design problems of electromagnetic devices. Improved SOM can simultaneously optimize the statistical approximate models and optimization algorithms more efficiently compared with SOM. Using DROM, a high dimensional problem can be converted into a low dimensional problem with expert experience or some design of experiment techniques. Then two TEAM benchmark problems (Problem 22 and Problem 25) are investigated to illustrate the efficiency of the proposed methods. From the experimental results, we can see that the presented methods can obviously reduce the computational cost of finite element analysis, while the optimal results also satisfy design specification.