## 4 Examples
### Three-Bay Ten-Story Framework
#### 4.2.1 Parameter Tuning in PFAM for the Three-Bay Ten-Story Framework
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{\(\gamma_{0}\)} & \multirow{2}{*}{**Mean**} \\ \cline{3-5} \cline{5-6}  & & **0.1** & **1** & **10** & **25** \\ \hline \multirow{5}{*}{\(\alpha_{0}\)} & 0.3 & 695.53 & 1006.48 & **51.63** & 578.95 & 583.15 \\ \cline{2-6}  & 0.4 & 5032.57 & 801.17 & 176.01 & 185.58 & 1548.83 \\ \cline{2-6}  & 0.5 & 1127.87 & 470.94 & 186.29 & 176.27 & **490.34** \\ \cline{2-6}  & 0.6 & 3371.61 & 693.22 & 121.17 & 273.67 & 1114.92 \\ \cline{2-6}  & 0.7 & 8076.86 & 285.18 & 151.78 & 196.01 & 2177.46 \\ \cline{2-6}  & 0.8 & 2910.99 & 876.56 & 666.37 & 792.41 & 1311.58 \\ \cline{2-6}  & 0.9 & 1196.02 & 1019.10 & 258.01 & 716.03 & 797.29 \\ \cline{2-6}  & 1.0 & 1076.03 & 352.63 & 669.74 & 116.06 & 553.62 \\ \hline \multicolumn{2}{c}{**mean**} & 2935.94 & 688.16 & **285.13** & 379.37 & \\ \hline \hline \end{tabular}
\end{table} 
Table 36: Three-bay ten-story framework with EEP2 semi-rigid connections. Sensitivity analysis for \(\alpha_{0}\) and \(\gamma_{0}\) Standard deviation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{\(m\)} & \multirow{2}{*}{**Mean**} \\ \cline{3-5} \cline{5-6}  & & **1** & **2** & **3** \\ \hline \multirow{5}{*}{\(t_{c}\)} & 0.1 & **275.28** & **213.71** & 1498.46 & **662.49** \\ \cline{2-6}  & 0.3 & 326.75 & 1018.38 & 1162.37 & 835.83 \\ \cline{2-6}  & 0.5 & 674.17 & 1015.90 & 1019.74 & 903.27 \\ \hline \multicolumn{2}{c}{**mean**} & **425.40** & 749.33 & 1226.86 & \\ \hline \hline \end{tabular}
\end{table} 
Table 34: Three-bay ten-story framework with EEP2 semi-rigid connections. Sensitivity analysis for \(t_{c}\) and \(m\). Standard deviation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{\(\gamma_{0}\)} & \multirow{2}{*}{**Mean**} \\ \cline{3-5} \cline{5-6}  & & **0.1** & **1** & **10** & **25** \\ \hline \multirow{5}{*}{\(\alpha_{0}\)} & 0.3 & 0.968874 & 0.977775 & **0.994244** & 0.988987 & 0.982470 \\ \cline{2-6}  & 0.4 & 0.944331 & 0.980527 & 0.993107 & 0.993071 & 0.977759 \\ \cline{2-6}  & 0.5 & 0.968911 & 0.982921 & 0.993255 & 0.992099 & **0.984297** \\ \cline{2-6}  & 0.6 & 0.949196 & 0.979579 & 0.990534 & 0.992214 & 0.977881 \\In summary, after performing these sensitivity analyses, the following was observed:  
1. the selected values of parameters \(nt=1000\) and \(k_{max}=100\) produced good metric results with low computational cost;
2. parameter \(t_{c}\) affected the exploration and exploitation phases of the algorithm, obtaining good metric values when values of parameter \(t_{c}\) of around 0.1 were adopted;
3. \(m\) values close to the unit produced good metric values for low \(t_{c}\) values; and
4. the values of parameter \(\gamma_{0}\) greater than the unit produced good metric values, with \(\alpha_{0}\) in the range [0.3, 1.0]. As a result of the sensitivity analyses performed in this example, PFAM initially seems efficient and robust for the parameter values in Table 37. However, these values have been checked in another problem to study PFAM's behavior and establish another level of robustness, namely that of the algorithm against changes in the problem. As in the previous example, a problem with rigid connections between members of the structure has been considered, for which only the design variables \(X_{1}\) to \(X_{20}\) are necessary (see Tables 29 and 30). With rigid connections, and the initial constant values \(\beta_{0}=1\), \(m=2\), \(\gamma_{0}=10\), \(\alpha_{0}=1\), and \(t_{c}=0.1\), the \(nt\) and \(k_{max}\) parameter values were modified. The accuracy results are shown in Table 38, and the standard deviation results are shown in Table 39.  
In Table 38, the maximum accuracy values have been highlighted in bold, as have the minimum values of standard deviation in Table 39. The shaded areas in both tables