Unlike the existing methods, the proposed rule of start point selection takes an advantage of minimizing the search time. A study has been conducted on the multi-purpose optimized design PMSM of fractional slotted windings [19]. The optimization results demonstrated the accuracy of the proposed model with comparison to numerical models such as FEA, but with much faster computational performance which makes it much more suitable to be used in evolutionary optimization design approaches. Most of the previous studies were applied to the optimal design using metamodels created in one way [20,21]. In general, FEA's design of experiment (DOE) consists of a modeling process using CADtools, an FEA analytical condition setting process, a FEA process, and a post-process for extracting and configuring results. A lot of DOE has to be done to get reliable and optimal design results. As a related study, Taguchi method was used to optimize the efficiency and cogging torque of BLDC motors used in automotive electric oil pumps. However, to obtain DOE results, 336 FE analyses for five design variables were required [22]. This study differs from previous studies given that five design variables were selected for the DOE and 54 experiments were performed. To improve the efficiency of the design variable distribution, the optimal Latin hypercube design (OLHD) [23; 24] was used with an equal number of levels for all the design variables that has a better fill performance than Latin hypercube design (LHD) [25]. Numerous studies have been published on metamodeling conducted based on the application of a single method [26; 27]. However, there are suitable metamodels for each optimal design problem. Correspondingly, the metamodels need to be written and compared in various ways. Given that the prediction performance of the metamodel affects the reliability of the optimal design, it is necessary to evaluate the accuracy of each metamodel. Therefore, we evaluated three representative metamodels, including Kriging [28], multilayer perceptron (MLP) [29], and ensemble of decision tree (EDT) [30], and compared the metamodeling results. The predicted performances of the metamodels were evaluated and compared based on the root-mean-square error (RMSE) test, the results, and Kriging was selected as the best metamodel. In this paper, Kriging model can evaluate models with many design variables, complex responses, or strong nonlinearities more accurately. The genetic algorithm (GA) [31] was used for the determination of the optimal design variables based on the objective functions and constraints set for the optimization. To verify the validity of the proposed optimization design results, the characteristics of the initial and the optimal models (back-electromotive force (EMF), cogging torque, and torque ripple) were evaluated based on finite element analyses, and the results were compared. To verify feasibility, the proposed optimization method was applied to the design of a 3 kW PMSM used in an electric compressor, and the method's performance was compared with the results obtained from the initial model with finite element analysis. Finally, prototype PMSMs were fabricated and dynamometer tests were performed to confirm the suitability of the proposed shape optimization design.