# Root-Crush Protection Design of Automotive Bodies Using Clustering and Pattern Recognition
## 4 Optimization
### Optimization Results  
The RSM was configured according to the traditional and proposed optimization methods listed in Table 5, and a genetic algorithm was used to optimize each case. The genetic algorithm has the disadvantage of requiring a lot of computation, but it has the advantage of not depending on an initial design point. Thus, there is little concern over it converging at a local optimum point, and parallel computation is possible. It also has the advantage of being applicable to almost all variable types as well as discontinuous problems. The predicted response obtained from the optimization results was compared with the actual response obtained from performing FEA on the model composed of optimized design variables obtained during optimization. Table 6 summarizes the optimization results for the case of a mass of 30 kg using 5 strong clusters from 15 clustering type. In this case, \begin{table}
\begin{tabular}{l l} \hline \hline  & **Traditional Optimization Method** \\ \hline (1) & Configure RSM using all 2000 models \\ (2) & Perform optimization under the following conditions: \\  & Objective function: Maximizing reaction force \\  & Constraints: Targeting mass (26, 27, 28, 29, 30 kg) \\ \hline \multicolumn{2}{c}{**Proposed Optimization Method**} \\ \hline (1) & Configure RSM using only \(N\) number of strong clusters obtained as \\  & clustering results \\ (2) & Perform optimization under the following conditions: \\  & Objective function: Maximizing reaction force \\  & Constraints: Targeting mass (26, 27, 28, 29, 30 kg) \& avoiding \(N\) \\  & weak clusters \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of traditional and proposed optimization techniques. 757 models were used for the RSM to calculate the optimized design variables and the corresponding reaction forces. In this study, all 2000 BIW models were clustered into three quantities of clusters: 10, 15, and 20, as shown in Table 4. Based on the optimization process in Table 5, the proposed optimization results were summarized in Table 7 for different clustering types (3, 5, and 7 strong clusters in the 10 clustering; 3, 5, 7, 8, 10, and 12 strong clusters in the 15 clustering; 3, 5, 7, 13, 15, and 17 strong clusters in the 20 clustering) with the 5 cases of targeting mass (26, 27, 28, 29, and 30 kg). In most cases, the maximal reaction forces obtained by the proposed optimization process were improved compared with the values by the traditional optimization. Here, OM values represent the calculated (predicted) results of the reaction force obtained using the proposed optimization method. Additionally, FEA values mean the actual reaction force calculated by a commercial finite element software, ABAQUS, using the optimal design variables obtained by the optimization process. The error rate is calculated by \(\mid\)OM - FEA \(\mid\)/OM (%). Figure 5 shows the improvements in the proposed optimization results for each cluster compared with the traditional optimization. Compared with the traditional method, when the RSM configuration used three strong clusters that were obtained from the 10 clusters (case 2 in Table 7), the overall improvement was 3.55%. When the RSM configuration used five strong clusters that were obtained from the 15 clusters (case 6 in Table 7), the overall improvement was 3.48%. When the RSM configuration used seven strong clusters that were obtained from the 20 clusters (case 13 in Table 7), the overall improvement was 4.64%. In the remaining cases, a small range of performance improvement was also confirmed.