## 5 Benchmark Numerical Example
### Initial Optimization Results  
Following the detailed description and validation of the benchmark numerical example, the initial optimization process was carried out using the developed framework to achieve a structurally safe and materially efficient design. The selected beam-to-column connection was designed based on an average force value derived from the load levels associated with configurations SC1-SC7 at a joint rotation of 0.025 rad. Consequently, the applied force was set to \(F=221.56\) kN. Furthermore, the volume of the SC7 connection was used as the reference maximum volume \(V_{max}\), while the allowable equivalent plastic strain was limited to \(\Xi_{max}^{pl}=0.05\) in accordance with EN1993-1-5 [35]. The joint rotation limit was also defined as \(\theta_{\max}=0.025\) rad, and the minimum required buckling load factor was set to \(\lambda_{stab}=1.00\). The design space was defined based on the parameters listed in Tables 5-7. Consistent with the numerical models, two primary connection types are considered during the optimization: flush and extended end-plates. In the case of extended end-plates, rib \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Configuration**} & \multirow{2}{*}{\(f\)**(V)**} & \multirow{2}{*}{\(\theta\) (rad)} & \multicolumn{2}{c}{**Force in the Experiment**} & \multicolumn{1}{c}{**Force in the Simulation**} & \multirow{2}{*}{\(F_{raw}\)/\(F_{FTM}\)} & \multirow{2}{*}{
\begin{tabular}{c} **Maximum Plastic** \\ **Strain \(\overline{x}^{pl}\) (\%)** \\ \end{tabular} } \\  & & & \(F_{exp}\) (kN) & & & \\ \hline SC1 & 0.7034 & & 136.07 & 128.66 & 1.058 & 3.62\% \\ SC2 & 0.8748 & & 227.86 & 237.62 & 0.959 & 3.37\% \\ SC3 & 0.8518 & & 212.61 & 202.98 & 1.047 & 3.32\% \\ SC4 & 0.5061 & & 224.07 & 218.83 & 1.024 & 3.28\% \\ SC5 & 0.9874 & & 255.37 & 265.89 & 0.960 & 3.87\% \\ SC6 & 0.8850 & & 234.46 & 248.48 & 0.944 & 5.53\% \\ SC7 & 1.0000 & & 273.14 & 282.11 & 0.968 & 3.17\% \\ SC8 & 0.7834 & & 208.89 & 205.10 & 1.018 & 5.36\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of the main results for the evaluated configurations. Figure 9: Comparison of the moment–rotation curves obtained from the experiment and the FE model for the different configurations: (**a**) SC1, (**b**) SC2, (**c**) SC3, (**d**) SC4, (**e**) SC5, (**f**) SC6, (**g**) SC7, and (**h**) SC8. stiffeners may be introduced along the top flange, bottom flange, or both, or they may be omitted entirely. Likewise, column stiffeners are permitted in various configurations--at the top, bottom, both locations, or not at all--aligned with the corresponding beam flange axes. Additionally, the bolt arrangement, including the number, position, and type, is treated as a variable. The end-plate thickness is also varied within a predefined range. This flexible parameterization enables the generation and exploration of a broad set of feasible configurations throughout the optimization process. It should also be noted that for bolt types, in addition to 20 mm and 24 mm diameters, the corresponding pretension forces were assigned in accordance with the guidelines specified in EN 1993-1-8 [11]. Once the design space was defined, the optimization process was carried out. It should be noted that during this process, each design configuration--defined by the variables presented earlier--was automatically generated and analyzed through a fully integrated framework. Each binary-encoded chromosome was automatically decoded, followed by the generation of the corresponding FE model and execution of the structural analysis. The results were then processed to evaluate the objective function, incorporating both the objective function and any applicable penalty terms. After calculating the fitness value for each potential solution, the genetic operators iteratively refined the population to improve the solutions until the stopping criterion was met. All components of this workflow were implemented within the custom-developed PYTHON code.