## 5 Process of Optimal Foil Width Determination and Results
### Results TP1
#### 5.1.2 Determination of Parameters \(a\), \(b\), and \(c\)
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Function F1**} & \multicolumn{4}{c}{**Used Foil WIDTH**} \\ \cline{2-5}  & **2 m, 4 m, 8 m** & **2 m, 5 m, 8 m** & **2 m, 6 m, 8 m** \\ \hline OF for three foil widths & 0 & 0 & 0 & \\ \(A\) & 3592.9 & 3331.8 & 3163.1 & \\ \(B\) & \(-927.0\) & \(-763.8\) & \(-658.4\) & \\ C & 67.71 & 51.39 & 40.85 & \\ \hline OF for all seven foil widths & \(2.0497\times 10^{-1}\) & \(5.7397\times 10^{-2}\) & \(8.1322\times 10^{-2}\) & \(\sum\)3.4369 \(\times\) 10\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Calculated parameters and OF for three foil widths and for all foil widths based on three foil widths for F1 using TP1 data. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**OF and Parameters**} & \multicolumn{4}{c}{**Method**} \\ \cline{2-7}  & **DE/rand/1/exp** & **DE/rand/2/exp** & **DE/best/1/bin** & **TLBO** & **ABC** \\ \hline  & B & 0 & 0 & 0 & \(4.5500\times 10^{-32}\) & \(5.9706\times 10^{-15}\) \\ OF3 & W & 0 & 0 & \(1.2388\times 10^{-32}\) & \(4.5500\times 10^{-32}\) & \(3.0295\times 10^{-13}\) \\ _fw_ 2, 5, 8 m & M & 0 & 0 & \(8.2592\times 10^{-34}\) & \(4.55\times 10^{-32}\) & \(3.7803\times 10^{-14}\) \\  & SD & 0 & 0 & \(3.0903\times 10^{-33}\) & \(2.7369\times 10^{-47}\) & \(5.9342\times 10^{-14}\) \\ \hline a & B & 4149.47 & 4149.47 & 4149.47 & 4149.47 & 4149.47 \\ \hline b & B & 0.4802 & 0.4802 & 0.4802 & 0.4802 & 0.4802 \\ \hline c & B & 421.66 & 421.66 & 421.66 & 421.66 & 421.66 \\ \hline \(t\) (s) & M & 31.7 & 32.1 & 30.8 & 40.5 & 24.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: OF3 and best value of the calculated parameters for 30 independent runs using F2 and \(U_{\text{Smax}}\) for \(fw\) = 2, 5, and 8 m of TP1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Function F4**} & \multicolumn{3}{c}{**Used Foil Width**} \\ \cline{2-4}  & **2 m, 4 m, 8 m** & **2 m, 5 m, 8 m** & **2 m, 6 m, 8 m** \\ \hline OF three foil widths & \(1.1067\times 10^{-27}\) & \(2.6596\times 10^{-28}\) & \(6.4597\times 10^{-27}\) \\ \(a\) & \(2796.49\) & \(2530.51\) & \(2369.74\) \\ \(b\) & \(-0.5997\) & \(-0.5265\) & \(0.4679\) \\ \(c\) & \(464.56\) & \(435.75\) & \(398.52\) \\ \hline OF all seven foil widths & \(1.6360\times 10^{-2}\) & \(1.0613\times 10^{-2}\) & \(3.3713\times 10^{-2}\) & \(\sum\)6.0686 \(\times\) 10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Calculated parameters and OF for three foil widths and for all foil widths based on three foil widths for F5 using TP1 data. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Function F5**} & \multicolumn{3}{c}{**Used Foil Width**} \\ \cline{2-4}  & **2 m, 4 m, 8 m** & **2 m, 5 m, 8 m** & **2 m, 6 m, 8 m** \\ \hline OF three foil widths & \(1.2799\times 10^{-32}\) & \(0\) & \(1.2389\times 10^{-32}\) \\ \(a\) & \(4707.45\) & \(4149.47\) & \(3773.83\) \\ \(b\) & \(-0.55378\) & \(-0.48021\) & \(-0.41956\) \\ \(c\) & \(454.63\) & \(421.66\) & \(379.15\) \\ \hline OF all seven foil widths & \(1.3186\times 10^{-2}\) & \(6.5036\times 10^{-3}\) & \(2.0229\times 10^{-2}\) & \(\sum\)3.9919 \(\times\) 10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Calculated parameters and OF for three foil widths and for all foil widths based on three foil widths for F2 using TP1 data. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Function F2**} & \multicolumn{3}{c}{**Used Foil Width**} \\ \cline{2-4}  & **2 m, 4 m, 8 m** & **2 m, 5 m, 8 m** & **2 m, 6 m, 8 m** \\ \hline OF three foil widths & \(1.12799\times 10^{-32}\) & \(0\) & \(1.2389\times 10^{-32}\) \\ \(a\) & \(4707.45\) & \(4149.47\) & \(3773.83\) \\ \(b\) & \(-0.55378\) & \(-0.48021\) & \(-0.41956\) \\ \(c\) & \(454.63\) & \(421.66\) & \(379.15\) \\ \hline OF all seven foil widths & \(1.3186\times 10^{-2}\) & \(6.5036\times 10^{-3}\) & \(2.0229\times 10^{-2}\) & \(\sum\)3.9919 \(\times\) 10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table}