## 4 Results and Discussion
### Hys_En Optimization According to Different Constraints  
A comparison of the energy components of PRA/PGA has been presented in previous sections. The structure responses show that Inp_En and R_En give the closest and most feasible results to \(PRA/PGA\). According to the results, the objective function can be chosen according to the structure response targeted by the designer. In this study, different \(D\) and \(\beta\) constraints are analyzed by using R_en, which minimizes the \(ISDR\) because the \(ISDR\) is the primary structural response used in terms of structural stability. For this purpose, the optimization processes were repeated with different limits and are given in Table 7. In this way, the effectiveness of the energy ratio in seismic isolation parameter optimization has been demonstrated. Optimization processes and ground motions are the same as in the previous sections. As illustrated in Table 7, the effective damping is increased while the displacement is simultaneously reduced. The optimum isolation parameters obtained for the new cases depending on R_En are presented in Table 8. The structure responses and critical ground motions calculated with the optimum isolation parameters are given in Table 9.  
As presented in Table 9, the structure responses are within the constraints for all R_En minimization cases. \(PRA/PGA\) increases as the constraint \(D\) decreases. Especially in the cases of R_En_45_40 and R_En_40_50, the increase in \(\beta\) is possible, but it is calculated around 30%. This result demonstrates that the R_En, similar to the PRA/PGA, is unable to \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{2}{c}{**Searching Isolation Parameters**} & \multicolumn{2}{c}{**Constraints**} \\ \cline{2-6}  & \(T_{0}\) **(s)** & \(F_{Q}\)/\(W\) & \(D\) **(m)** & \(\beta\) **(\%)** & **ISDR** \\ \hline R\_En\_50\_30 & & & \(<\)50 & \(<\)30 & \\ R\_En\_45\_40 & 2–4 & 0.03–0.15 & \(<\)45 & \(<\)40 & 0.01 \\ R\_En\_40\_50 & & & \(<\)40 & \(<\)50 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimization parameters using R_En as the objective function. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **T0 (s)** & **FQ/W** \\ \hline R\_En\_50\_30 & 3.041 & 0.07421 \\ R\_En\_45\_40 & 2.755 & 0.09069 \\ R\_En\_40\_50 & 2.619 & 0.11517 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The optimum isolation parameters obtained with the R_En objective function. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case** & **Objective Function Result (kNm)** & **Critical Ground Motion** & \(D\) **(m)** & \(\beta\)**(\%)** & **ISDR** & **PRA/PGA** \\ \hline R\_En\_50\_30 & 44.68 & Duzce & 0.4970 & 29.978 & 0.00813 & 1.209 \\ R\_En\_45\_40 & 46.80 & Duzce & 0.4398 & 30.157 & 0.00893 & 1.399 \\ R\_En\_40\_50 & 51.38 & Duzce & 0.3999 & 31.495 & 0.00953 & 1.566 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The results of the optimal isolation parameters in critical ground motion with varying constraints using the R_En objective function. determine the optimum result from high values of \(\beta\). In addition, as the displacement limit increased, \(PRA/PGA\) increased and \(ISDR\) decreased. The convergence curves with R_En regarding their most favorable runs in three different constraint cases are given Figure 10.  
It can be seen that the optimum energy ratio is reached with the GWO in all R_En cases. Search agents start with a random solution initially, and the optimum energy is reached on average at the 40 th iteration. The approximation curves demonstrate that R_En_ 50_30 converges fastest to the minimum energy ratio. Story accelerations and \(ISDR\) graphs for the optimum isolation parameters of R_En cases are presented in Figure 11. The results are given according to Tabas, which represents the most unfavorable ground motion in the structure generated by the optimized isolation parameters.