## 3 Examples
### Cross-Section under Flexure
The performance metrics are also shown in Figures 5-7. It can be observed that the metrics tend to worsen in all cases when the number of subpopulations increases. This tendency is greater when LSRD is used alone and above eight subpopulations. The other cases have a lower tendency. The sensitivity of the metrics with respect to the number of subpopulations is reduced when LSRD and GSRD are taken into account at the same time. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subpopulations** & **Mean Cost** & **Accuracy** & **Robustness** \\ \hline
1 & 85.81 & 0.9969 & 0.51 \\
2 & 85.73 & 0.9977 & 0.43 \\
3 & 85.71 & 0.9980 & 0.39 \\
4 & 85.73 & 0.9978 & 0.43 \\
5 & 85.73 & 0.9978 & 0.41 \\
6 & 85.65 & 0.9988 & 0.27 \\
7 & 85.71 & 0.9980 & 0.37 \\
8 & 85.81 & 0.9968 & 0.51 \\
9 & 85.99 & 0.9947 & 1.05 \\
10 & 86.24 & 0.9918 & 1.43 \\
11 & 85.85 & 0.9964 & 0.62 \\
12 & 85.96 & 0.9951 & 0.99 \\
13 & 86.06 & 0.9939 & 0.94 \\
14 & 86.20 & 0.9923 & 1.20 \\
15 & 86.32 & 0.9910 & 1.51 \\
16 & 86.29 & 0.9914 & 1.38 \\ \hline
**Averaged value** & 85.93 & 0.9955 & 0.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Cross-section under flexure. LSRD and GSRD. Performance metrics. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subpopulations** & **Mean Cost** & **Accuracy** & **Robustness** \\ \hline
1 & 85.81 & 0.9969 & 0.51 \\
2 & 86.08 & 0.9937 & 0.66 \\
3 & 85.93 & 0.9955 & 0.62 \\
4 & 85.73 & 0.9978 & 0.43 \\
5 & 85.74 & 0.9976 & 0.45 \\
6 & 85.74 & 0.9976 & 0.46  
Figure 5: Cross-section under flexure. Mean cost. Figure 6: Cross-section under flexure. Robustness. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** \\ \hline \(\varphi^{\prime}y=\varphi_{y}=\varphi^{\prime}x=\varphi_{x}\) & \(\varphi^{\prime}y=\varphi_{y}\) & \\ \(n^{\prime}y=n_{y}\) & \(\varphi^{\prime}x=\varphi_{x}\) & \\ \(n^{\prime}y=n_{y}\) & \(n^{\prime}y=n_{y}\) & \\ \(n^{\prime}x=n_{x}\) & \(n^{\prime}x=n_{x}\) & \\ \hline \(z\)(mm) & - & 269.9 & 250.4 & 280.3 \\ \(\theta\)(rad) & - & 0.8660 & 1.0035 & 1.1029 \\ \(b\)(mm) & - & 495 & 460 & 465 \\ \(h\)(mm) & - & 575 & 620 & 615 \\ \(\varphi^{\prime}y\)(mm) & - & 12 & 12 & - \\ \(n^{\prime}y\) & - & 8 & 2 & - \\ \(\varphi_{y}\)(mm) & - & 12 & 12 & 10 \\ \(n_{y}\) & - & 8 & 2 & 10 \\ \(\varphi^{\prime}x\)(mm) & - & 12 & 32 & 10 \\ \(n^{\prime}x\) & - & 10 & 2 & 2 \\ \(\varphi_{x}\)(mm) & - & 12 & 32 & 16 \\ \(n_{x}\) & - & 10 & 2 & 9 \\ \hline \(A_{st}\)(mm\({}^{2}\)) & - & 4070.2 & 3667.0 & 2752.0 \\ Relative \(A_{st}\)(\%) & - & 100.0 & 90.1 & 67.6 \\ \hline \(\text{Cost}\)(\(\ell\)/m) & - & 98.5 & 95.1 & 86.6 \\ Relative cost (\%) & - & 100.0 & 96.5 & 87.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optimal design solutions with variable section. EC2. \begin{table} \begin{tabular}{c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** \\ \hline \(\varphi^{\prime}y=\varphi_{y}=\varphi^{\prime}x=\varphi_{x}\) & \(\varphi^{\prime}y=\varphi_{y}\) & \\ \(n^{\prime}y=n_{y}\) & \(\varphi^{\prime}x=\varphi_{x}\) & \\ \(n^{\prime}x=n_{x}\) & \(n^{\prime}y=n_{y}\) & \\ \(n^{\prime}x=n_{x}\) & \(n^{\prime}x=n_{x}\) & \\ \hline \hline \end{tabular}  \ \begin{tabular}{c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** \\ \hline \(\varphi^{\prime}y=\varphi_{y}=\varphi^{\prime}x=\varphi_{x}\) & \(\varphi^{\prime}y=\varphi_{y}\) & \\ \(n^{\prime}y=n_{y}\) & \(\varphi^{\prime}x=\varphi_{x}\) & \\ \(n^{\prime}x=n_{x}\) & \(n^{\prime}y=n_{y}\) & \\ \(n^{\prime}x=n_{x}\) & \(n^{\prime}x=n_{x}\) & \\ \hline \hline \end{tabular} 
\begin{tabular}{c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** \\ \hline \(\varphi^{\prime}y=\varphi_{y}=\varphi^{\prime}x=\varphi_{x}\) & \(\varphi^{\prime}y=\varphi_{y}\) & \\ \(n^{\prime}y=n_{y}\) & \(\varphi^{\prime}x=\varphi_{x}\) & \\ \(n^{\prime}y=n_{y}\) & \(\varphi^{\prime}x=\varphi_{x}\) & \\ \(n^{\prime}x=n_{x}\) & \The average time of 50 runs, considering ACI318 standard and using MPFA with different numbers of subpopulations, was obtained.