## 3 Model Complexity and Space Reduction Techniques for System-Level Optimization
### Sequential Subspace Optimization Method
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ref.** & **Modeling** & **Optimization** & **System-Level** & **Optimization** & **Optimization** & **Application** \\  & **Algorithm** & **Algorithm** & **Machine/Control** & **Machine/Control** & **Goals** & **Application** \\ \hline
[14] & RSM with SA & DE & & & Geometrical & Torque Ripple, & In-Wheel \\  & & & & \(\theta_{on},\theta_{off}\) & Losses & application EV \\ \hline
[24] & RSM & FIS–NSGA-III & & & Geometrical & Efficiency, Torque & \\  & & & & Parameters/\(\theta_{on},\theta_{c}\) & Ripple, Power & SRG Drives \\ \hline
[25] & FEM & GA & Single-Level & & Candidate & Average Torque, & Vertical \\  & & & & Models/\(\theta_{on},\theta_{off}\) & Torque Ripple & Transportation \\ \hline
[26] & FEM & PSO & & & Efficiency, Torque & \\  & & & & Ripple, Power & SRM Drives \\ \hline
[27] & Field-Circuit-coupled FEM & GA & & & Density & Efficiency, Mass & Aerospace \\ \hline
[28,31] & [28] FEM, [31] & [28] NSGA-II, FEM with SA & [31] GA & [28] Single-Level, & \(\theta_{on},\theta_{off}\) & Average Torque, & [28] In-Wheel & application EV, \\ \hline
[30] & Kriging & NSGA-II & & & Average Torque, & \\  & & & & Torque Density, & EV \\ \hline
[34] & PR Model & MOGA & & & \(\theta_{on},\theta_{off}\) & Average Torque, & \\ \hline
[36] & Kriging & NSGA-II & & & \(\theta_{on},\theta_{c}\) & Average Torque, & \\  & & & & \(\theta_{on},\theta_{c}\) & Torque Ripple, & RMS Current & SRM Drives \\ \hline
[37,38,66] & Kriging with SA & [37,38] & Single-Level & & [37] Rotor pole shape, [38,66] & Average Torque, & \\  & & & & Geometrical & Torque Ripple, & \\  & & & & Parameters/ & Losses & \\ \hline
[39] & Kriging with SA & GRA with TOPSIS & Multi-Level & & Average Torque, & \\  & & & & Torque Ripple, & Losses & \\ \hline
[40] & FEM with & & & Geometrical & Average Torque, & EV \\  & & & & Parameters/ & Losses, & \\  & & & & Temperature Rise & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of references on system-level design optimization of SRMs. Regarding the optimization algorithms employed, the most widely used are NSGA-II and GA, due to their strong capabilities in handling non-linearities and their robust search ability and adaptability, making them well-suited for multi-objective problems. On the other hand, various innovative algorithms can be introduced to SRM drive system optimization to reduce computational time. One such method is the Decentralized Stochastic Recursive Gradient (DSRG) algorithm, which has the ability to split the overall problem into smaller, manageable subproblems, solving them in parallel and thereby significantly reducing computational effort. Furthermore, its stochastic gradient updates are particularly effective in navigating the non-linear nature inherent in SRM design [67]. Another promising approach is the Black Widow Optimization (BWO) algorithm [68], which offers fast convergence and can address both non-linearities and multi-objective problems, features especially relevant in complex SRM drive systems. All the aforementioned studies fall under the category of System-Level Optimization, as they analyze and optimize both the machine and the controller simultaneously or sequentially using various methods discussed earlier. However, these studies primarily focus on optimizing machine-related parameters such as torque, losses, efficiency, and torque ripple, while neglecting key controller performance metrics such as speed overshoot, settling time, controller efficiency and losses, which are left to be adjusted by the controller's algorithm. Moreover, the only controller-related parameters considered in the optimization process are the turn-on, \(\theta_{on}\), turn-off, \(\theta_{off}\), and conduction, \(\theta_{c}\), angles. To the authors' best knowledge, there are no existing recent studies that incorporate a broader range of controller performance metrics in SLDOM for SRM drives.