## 3 Model Complexity and Space Reduction Techniques for System-Level Optimization
### Sequential Subspace Optimization Method  
The Sequential Subspace Optimization Method (SSOM) is an approach that falls under the category of multi-level optimization, as it performs optimization across multiple levels by dividing the overall search space. In contrast to the single-space optimization method, which conducts optimization on a single level considering all design parameters simultaneously, the multi-level approach divides the problem into separate yet related subspaces in which the parameters defined for optimization are placed into based on their significance, with each subspace being optimized separately. This process is sequential, and at each level, the parameters of the other levels remain fixed. The entire process is iteratively repeated until a convergence criterion is met [11]. Figure 10 shows the SSOM framework, with the most critical parameters placed in the first level, and the least critical ones assigned to the final level. This method is particularly useful in cases where the number of optimization parameters and the solution search space are extensive, such as in System-Level Optimization [11; 63; 64]. Classification of parameters based on their significance is performed through sensitivity analysis, which evaluates the impact of small variations in each parameter on the overall system performance [63]. Initially, the authors of [20; 65] mapped the SLDOM framework and enhanced it with the SSOM and surrogate models, such as Kriging, combined with a sensitivity analysis. In [20], the optimization results are promising, showing an increase in output power, torque, and efficiency, while reducing cost, torque ripple, and losses. Additionally, the computational time with the SSOM has been reduced by up to five times for the motor and twice for the control compared to a single-level optimization method. In references [37; 38; 40], system parameters are categorized into three levels--highly significant, significant, and non-significant--based on their criticality, followed by sequential subspace optimization. In [37], the sensitivity analysis identifies the controller turn-on, \(\theta_{on}\), and turn-off, \(\theta_{off}\), angles as the most critical parameters, placing them in the X1 subspace. Conversely, in [38], the control and motor parameters are distributed across the three levels, with each level requiring fewer FEM simulations for optimization and only three iterations for the whole optimization process, highlighting the significance of the SSOM approach. Finally, in [40], the Kriging model is utilized in combination with sensitivity analysis and the SSOM to accelerate the optimization process. The parameters identified through sensitivity analysis are divided into three levels, with the most critical being the turn-off \(\theta_{off}\) angle and the air gap \(g\). Only two iterations are required for the optimization algorithm to converge based on the termination criterion defined by the authors, resulting in a 16.17% improvement in overall system performance. Figure 10: Sequential subspace optimization method. In [66], the SSOM is utilized alongside the Kriging model and a local sensitivity analysis to optimize an SRM drive system. The design parameters are classified into the three subspaces, while the NSGA-II generates Pareto-optimal solutions through optimization. A termination criterion, based on the relative error between two successive iterations, determines the best design, leading to a 42% increase in torque and a torque ripple reduction of around 65%. Only three iterations are required for the termination criterion to be satisfied, with each subspace requiring significantly less time for optimization compared to the first. This is logical, as the most critical parameters, which have the greatest impact on system performance, are placed in the first subspace. The last comment highlights the significance of parameter criticality assessment, which refers to identifying the critical parameters and downplaying the influence of those with limited impact.