# Efficiency Optimization of the Main Operating Points of an EV Traction Motor
## 3 Optimal Design
### Optimal Design Results  
The optimal metamodels for the selected objective and constraint functions were combined with optimal design algorithms to derive the optimal points. Micro Genetic Algorithm (MGA), a type of Evolutionary Algorithm (EA), employs a small population size to achieve fast exploration and convergence [33]. Similarly, the Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES), another type of EA, improves the convergence speed using a multivariate normal distribution [34]. Progressive Approximate Discrete Optimization (PADO) addresses discrete optimization problems by progressively refining approximate solutions [35], and the Hybrid Metaheuristic Algorithm (HMA) is a global optimization algorithm [36]. The optimal design was determined using four algorithms, and the results are summarized in Table 8.  
When employing the MGA algorithm for optimal design, the efficiency at the main operating points, which was the objective function, exhibited the most significant increase and was thus selected as the optimal point. FEA was performed on the optimal point to verify the accuracy of the metamodel predictions and the validity of the optimal design. Table 9 compares the results obtained by the metamodel and FEA, as well as those of the initial and optimal models. As a result of the optimal design, the efficiency at the main operating points increased by 1.4% compared with the initial model, with an increase of 0.83% at MOP1, 0.47% at MOP2, and 0.09% at MOP3, as shown in Figure 9. \(THD_{Back-EMF}\) decreased by 1.13%, and Figure 10 compares the back electromotive force waveforms of the initial and optimal models. \(T_{Max,maxRPM}\) increased by 6.69 Nm; however, \(T_{Max,BaseRPM}\) did not meet the constraint of 251 Nm. This is because the allowable tolerance limit (Violated Constraint Limit) in the optimization software PIAnO 2024 was set to 1%. An excessively low or absent allowable tolerance limit can lead to a lengthy, nonconvergent optimization process, resulting in sub-optimal solutions. \(V_{line-to-line}\) and \(T_{ripple}\) satisfied the constraints; therefore, the model derived by combining the metamodel and MGA algorithm was determined to be the optimal model, and its geometry is shown in Figure 11. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Items** & **EDT** & **KRG** & **MLP** & \begin{tabular}{c} **PRG** \\ **(BS)** \\ \end{tabular} & \begin{tabular}{c} **PRG** \\ **(FS)** \\ \end{tabular} & \begin{tabular}{c} **PRG** \\ **(FQ)** \\ \end{tabular} & \begin{tabular}{c} **PRG** \\ **(LR)** \\ \end{tabular} & \begin{tabular}{c} **PRG** \\ **(SC)** \\ \end{tabular} & \begin{tabular}{c} **PRG** \\ **(SQ)** \\ \end{tabular} & \
\begin{tabular}{c} **RBF** \\ **(Int)** \\ \end{tabular} &
\begin{tabular}{c} **RBF** \\ **(Reg)** \\ \end{tabular} \\ \hline MOP1 & 0.0155 & 0.0129 & 0.0559 & 18.9496 & 0.0471 & 0.0479 & 0.0675 & 0.0479 & 0.0772 & 0.0608 & 0.0519 \\ MOP2 & 0.0608 & 0.0287 & 0.153 & 0.0361 & 0.0361 & 0.0436 & 0.0714 & 0.0436 & 0.0889 & 0.0648 & 0.0708 \\ MOP3 & 0.0549 & 0.0335 & 0.0643 & 0.0428 & 0.0418 & 0.048 & 0.0682 & 0.048 & 0.0775 & 0.0596 & 0.0418 \\ \(THD_{Back-EMF}\) & 0.2932 & 0.3955 & 0.5494 & 0.837 & 0.7324 & 1.075 & 1.8461 & 1.075 & 1.5921 & 0.6765 & 1.0536 \\ \(T_{Max,BaseRPM}\) & 3.4306 & 3.2366 & 1.9608 & 2.3048 & 2.3048 & 1.9746 & 5.1139 & 1.9746 & 2.877 & 1.0895 & 2.2645 \\ \(T_{Max,maxRPM}\) & 6.1921 & 3.3484 & 3.9595 & 0.6987 & 8.932 & 9.73 & 8.5624 & 9.73 & 9.3322 & 15.3482 & 0.9585 \\ \(V_{line-to-line}\) & 4.8343 & 4.9383 & 3.0527 & 6.1588 & 5.5731 & 5.0595 & 9.315 & 5.0595 & 6.9336 & 3.6986 & 3.4286 \\ \(T_{ripple}\) & 0.0202 & 0.0275 & 0.0168 & 0.0273 & 0.0324 & 0.0243 & 0.0474 & 0.0243 & 0.0414 & 0.0268 & 0.0246 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: RMSE test results.