A Robust Multimodal Optimization Algorithm Based on a Sub-Division Surrogate Model and an Improved Sampling Method

The characteristics analysis of an electric machine requires the finite-element method. Hence, a large amount of computation occurs in the design process to take into account uncertainties as the manufacturing tolerances. In this paper, an efficient and useful multimodal optimization algorithm using the kriging surrogate model is proposed for the robust optimization of an electric machine. However, the conventional kriging (CK) method has a memory problem in multi-dimensional problem due to the enlarged correlation matrix. Thus, a sub-domain kriging (SDK) strategy and improved Latin hypercube sampling (ILHS) are proposed not only to solve the memory problem of the CK method, but also to increase the convergence speed. In addition, a gradient-free sensitivity index is proposed for robust optimization in order to address the conventional first and second gradient index which causes a numerical error. The outstanding performance of the proposed algorithm is verified by comparing with other optimization methods via several mathematical test functions which includes multi-dimensional problem. Moreover, the proposed algorithm is applied to a cogging torque reduction design case for interior permanent magnet motor.