In order to ensure the output performance and suppress electromagnetic vibration of a hollow shaft permanent magnet brushless DC motor (HSPMBLDCM), a surrogate assisted model optimization method based on nonlinear multiple regression is proposed. Firstly, the optimal space filling sampling is determined by the Audze-Eglajs (AE) algorithm, and four main variables are selected by the Kernel Principal Components Analysis (KPCA) algorithm to construct the surrogate model. Next, the surrogate model was constructed using nonlinear multiple regression, and the R2 values of the coefficients of determination were all greater than 0.9, which verified the accuracy of the proxy model. Finally, the Robust Multiobjective Optimization Evolutionary Algorithms (RMOEA) were used to solve the surrogate model, and the optimal stator slot parameters were obtained. The results show that by optimizing the stator slot parameters, the average torque of the motor is reduced by 1.3%, which does not affect the output performance, and the maximum vibration acceleration of the motor at no load and rated load is reduced by 19% and 34.5%, respectively, which effectively reduces the electromagnetic vibration and proves the effectiveness and reliability of the optimization method. It provides an alternative means for motor vibration damping design optimization with outstanding practical significance.