## 4 Results and Discussion
### Comparison of Optimum Isolation Parameters for Energy Components and PRA/PGA  
The peak objective function value and constraint from each of the \(11\) earthquake records were determined in each iteration, and the most unfavorable result was presented. The optimum isolation parameters obtained with objective functions (Hys_En, Imp_En, R_En, and PRA/PGA) are summarized in Table 5.  
According to Table 5, it is observed that the optimum isolation parameters are close to each other. Especially, while the input energy, energy ratio, and PRA/PGA are quite close to each other, the hysteretic energy is relatively different. The objective function value, critical ground motion, \(D\), \(\beta\), and \(ISDR\) calculated as a result of the optimum isolation parameters are presented in Table 6.  
It can be said that the optimum parameters in all cases in Table 6 are within the constraints. While Hys_En could not reach the displacement constraint, it achieved the maximum \(PRA/PGA\) in all cases. For the maximization of hysteretic energy, \(D\) was determined less than other cases. However, this result also revealed the largest PRA/PGA value among the cases. The limiting constraints for Hys_En are determined as \(\beta\) and \(ISDR\). Although the Imp_En and R_En results are quite similar, the critical ground motions are in Denali and Duzce, respectively. The lowest \(ISDR\) result is in R_En, while the lowest peak roof/peak ground acceleration is in the PRA/PGA case, as expected. According to the PRA/PGA result, \(\beta\) did not reach the constraint limit, but found the lowest \(PRA/PGA\) \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Objective Function Result** & **Critical Ground Motion** & \(D\) (_m_) & \(\beta\) (\%)** & **ISDR** & **PRA/PGA** \\ \hline Hys\_En & 16,098 kNm & Hektor & 0.4085 & 29.868 & 0.00999 & 1.594 \\ Imp\_En & 18,802 kNm & Denali & 0.4998 & 29.352 & 0.00815 & 1.198 \\ R\_En & 44.68\% & Duzce & 0.4970 & 29.978 & 0.00813 & 1.209 \\ PRA/PGA & 1.184 & Denali & 0.4997 & 25.196 & 0.00847 & 1.184 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of optimum isolation parameters in critical ground motion with Hys_En, Imp_En, R_En, and PRA/PGA. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **T0 (s)** & \(F_{\textbf{Q}}\)/**\(W\)** \\ \hline Hys\_En & 2.498 & 0.10780 \\ Imp\_En & 3.025 & 0.07135 \\ R\_En & 3.041 & 0.07421 \\ PRA/PGA & 2.854 & 0.05797 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The optimum isolation parameters obtained with objective functions. compared to other cases. Increasing the \(\beta\) increased the \(PRA/PGA\), which is consistent with previous studies [20]. The function evaluations, which plot the best result calculated by the objective functions throughout the iterations, are presented for each optimization case in Figure 6.  
To measure the effectiveness of the optimization process, it is important to examine the curves that show the convergence to the optimum result over the iterations. It can be seen that, in all cases, the objective functions tend to mostly decrease to a suitable value after 10-40 generations, indicating that the GWO has a very good convergence property. Figure 6a is different from other convergence curves as it maximizes the hysteretic energy dissipations. In addition, when all approach curves were examined, it was determined that the fastest result was found by R_En. Effectiveness of Energy Components in the Optimization Process  
In this section, the results obtained from the energy components determined as the objective function are compared with the PRA/PGA results. As a result of the optimum isolation parameters obtained for different cases, the structure responses and energy components according to ground motions are given in Figure 7.  
When Figure 7 is examined, Hys_En is different from the other results. The highest results were calculated for \(PRA/PGA\), effective damping (\(\beta\)), input energy, and hysteretic energy.