## 4 Examples
### Analysis and Discussion of the Results  
In the first example, an extensive sensitivity analysis was carried out using PFAM. Different values were considered for a couple of parameters within extensive ranges, establishing those obtaining better metrics as tuned values. With tuned values, another pair of parameters were modified. This procedure was carried out several times. As expected, a strong interdependence among the parameter values was observed because the tuned values for a couple of them depended on the constant values chosen for the rest of the parameters. Therefore, adjusting parameters through simple procedures, such as the one shown here, is an arduous task that requires time and has a high computational cost. In the second example, a less extensive sensitivity analysis was carried out, as it was only intended to check the robustness of PFAM when different design cases are considered. At the end of the process, small differences were found in the tuned values of parameters \(t_{c}\), \(\alpha_{0}\), and \(m\) when comparing the results obtained in both examples with rigid and semi-rigid connections. However, greater differences were found in the tuned values of parameters \(\gamma_{0}\) and \(nt\). This situation could create uncertainty for future users when applying PFAM to the design of a new structure that differs considerably from previously designed structures. The PCPFAM selects the values of one or several parameters that maximize changes in landscape \(F_{i}\) during the design process. However, the parameters can be classified into two groups: those that can change during the process (\(\beta_{0}\), \(\alpha\), \(\gamma\), \(m\)) and those chosen at the beginning of the process that do not change during the process (\(t_{c}\), \(nt\), \(k_{max}\)). PCPFAM can only act on the former. The uncertainty in the choice of \(\gamma\) was resolved using PCPFAM. After having carried out the different sensitivity analyses with PFAM, some tuned and untuned values of the rest of the parameters were adopted in PCPFAM with a constant value during the process. The results showed that the algorithm obtained good metrics when parameter \(\gamma\) was changeable during the design process, which made the algorithm more robust. However, there is still uncertainty in the choice of parameter \(nt\). The adjusted values obtained through the sensitivity analyses carried out with PFAM show that \(nt\) depends on \(nv\), with very different values in each of the examples. Figure 32: Three-bay ten-story framework with rigid connections. PCPFAM. Evolution of parameter \(\gamma\). \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**PCPFAM**} \\ \hline
**EEP2 Semi-Rigid Connections** & \multicolumn{2}{c}{**Rigid Connections**} \\ \hline
**Accuracy** & **Standard Deviation** & **Accuracy** & **Standard Deviation** \\ \hline
0.992651 & 207.15 & 0.995769 & 389.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 46: Three-bay ten-story framework. PCPFAM. Accuracy and Standard deviation. To eliminate the uncertainty in the choice of parameter \(nt\), its dependence on \(nv\) was studied. First, the total number of possible designs (TNPD) in the examples was calculated as variations with repetitions of \(ne\) elements taken from \(nve\) to \(nve\). In the two examples, 24 (\(ne=24\)) HEB steel shapes were considered for the columns and 18 (\(ne=18\)) IPE steel shapes for the beams. When there were semi-rigid connections in the examples, 10 (\(ne=10\)) different types of steel bolts and 12 (\(ne=12\)) different types of steel end-plates were also considered. In the examples, \(nve\) is the number of variables used for the HEB and IPE shapes and the steel bolts and steel end-plates (see Tables 2, 3, 29 and 30). Thus, the TNPD in all the examples are included in Table 47. As can be seen, \(ne\) does not vary in the different cases, and \(nve\) does. Furthermore, the TNPD is a large number in all the cases. Therefore, it seems reasonable to use logarithms, although doubts arise about the base to use.