## 6 Results  
### Hull Form Optimization Results  
Based on the methodology described in the previous sections, the hull form optimization of KCS was conducted to minimize the total resistance coefficient of model \(C_{TM}\) at design draft and design speed \(Fn=0.260\). During the SQP optimization process, the running attitude was fixed to the values for the original hull. By using 432 CPU cores, the gradients with respect to nine design variables were calculated simultaneously. After 10 iteration steps, the \(C_{TM}\) was converged to minimum value and total computational time was 44 h including the original hull form calculation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Running Attitudes**} & \multicolumn{2}{c}{**Computational**} & \multirow{2}{*}{**Parallel**} & \multirow{2}{*}{**Number of CPU**} & \multirow{2}{*}{**Number of Simulations**} & **Total** \\  & **Time for Each** & & & & **Computational** \\  & **Simulation (h)** & & & & **Time (h)** \\ \hline Free & 5 & No & 24 & 190 & \(5\times 190=950\) \\ Fixed with static & 2 & No & 24 & 190 & \(2\times 190=380\) \\ Free & 5 & Yes & 432 & 20 & \(5\times 20=100\) \\ Fixed with static & 2 & Yes & 432 & 20 & \(2\times 20=40\) \\ sinkage \& trim & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Considerations on the computational time for hull form optimization. Figure 6: Definition of initial values for SQP. (a) SAC; (b) Waterline shapes at \(Z_{D}\) and \(Z_{L}\). Table 8 lists the convergence history of the \(C_{TM}\), the pressure resistance coefficient \(C_{P}\) and the frictional resistance coefficient \(C_{F}\). The iteration 0 denotes the original hull form calculation and the iteration 10 corresponds to optimal hull form, which yielded 1.8% reduction in \(C_{TM}\). The subscript 0 denotes the original value, so \(C_{TM}/C_{TM0}\) represents the ratio of \(C_{TM}\) between modified hull and original hull. The time histories of \(C_{TM}/C_{TM0}\) and \(C_{P}/C_{P0}\) are plotted with respect to the iteration number in Figure 7. As seen, the reduction in \(C_{TM}\) is closely associated with the reduction in \(C_{P}\) and occurs mainly until the 4 th iteration. The amount of reduction in \(C_{TM}\) in the initial phase until the 4 th iteration appears to be about 70% of total improvement. Body plans of three hull forms at iteration step 0 (original), 4, and 10 (optimal) during the optimization process are presented in Figure 8. The comparison between original and iteration 4 in Figure 8a demonstrates how the hull form is modified in the initial optimization period. It appears that the volume in the entrance part ahead of 17 ST increased whilst the volume in the shoulder part after 17 ST decreased. In order to keep the displacement unchanged, the amount of volume increase in some part should be balanced by the same amount of volume increase in the other part of the hull. A closer inspection reveals that the volume increase in the entrance part is distributed mainly around the bulbous bow near \(Z_{L}\) rather than at the design draft \(Z_{D}\). Figure 8b represents the hull form modification during the latter period of optimization. It is observed that the trend of initial hull form modification is still preserved except that the volume near \(Z_{D}\) in the entrance part has been slightly diminished.