## 5 Conclusions  
Recently, the investigation of the energy-based seismic design of structures has become a well-studied topic by researchers. The majority of the energy transmitted to conventional structures by earthquakes is dissipated by the structural members in the form of kinetic and viscous damping. Seismic isolation systems, which provide supplemental damping to the structure, dissipate the most of the input energy to the structure throughout the hysteretic motion process. Thus, the transfer of viscous energy, which has the potential to cause damage to the superstructure, is prevented. The consideration of input and hysteretic energy in the design of seismic isolation systems helps improve the response of base-isolated structures. This study aims to optimize seismic isolation systems via energy components. The seismic isolation parameters were optimized based on the minimization/maximization of the input and hysteretic energy with a GWO. In addition, the energy ratio (R_En), calculated via the ratio of the difference between the input energy (Inp_En) and the hysteretic energy (Hys_En) to the input energy, was utilized as the objective function. The obtained results were compared with optimized isolation parameters by PRA/PGA. The example base-isolated building was modeled numerically in ETABS software, and a time history analysis with 11 scaled ground motions was performed. The specific findings are summarized below based on the results:  
* The optimized seismic isolation parameters are within the predefined constraints in terms of structural response for all cases by the proposed energy-based methodology. * The optimization study performed on a seismically isolated 3D structure demonstrated that the three selected energy-based objective functions can successfully achieve optimum isolation system parameters satisfying the specified design constraints when compared with the optimization results of the PRA/PGA case. * When Imp_En, Hys_En, and PRA/PGA are used as objective functions, the optimum values of the isolation parameters are mainly controlled by the isolation displacement (\(D\)). On the other hand, the Hys_En optimization process is controlled by the effective damping (\(\beta\)) and the inter-story drift ratio (\(ISDR\)). * According to the effects of the scaled ground motions, the maximum acceleration and displacement were caused by Denali and Duzce ground motions, respectively. Duzce controlled the constraint by causing the maximum \(\beta\) compared to other ground motions due to its low displacement value. * It was observed that Imp_En and R_En were calculated with a high correlation in terms of optimum isolation parameters and structure responses. However, even if the \(ISDR\) of Imp_En is higher than R_En, the ratio of peak roof acceleration to ground peak acceleration (\(PRA/PGA\)) is low. So, the designer can obtain the optimum isolation parameters by selecting the appropriate objective function. * In this study, R_En was selected as the objective function on account of its advantage in terms of \(ISDR\), and the optimization process was conducted once more by employing a variety of constraints. \(ISDR\) and \(PRA/PGA\) were calculated to be lower than the other cases due to the high \(D\) constraint of the R_En_50_30 case. In addition, \(\beta\) was calculated at around 30%, although there is a possibility of an increase in terms of constraint. The authors believe that the outcomes of energy-based seismic isolation parameter optimization will contribute to expanding the literature on energy-based seismic design and more efficient isolator modeling. In the future, the modeling by energy-based methods of base-isolated actual projects might be included in seismic codes. resources, A.E.C. ; data curation, A.E.C. ; writing--original draft preparation, A.E.C. and N.K.C. ; writing--review and editing, A.E.C. and N.K.C. ; visualization, A.E.C. ; supervision, A.E.C. ; project administration, A.E.C. ; funding acquisition, A.E.C. All authors have read and agreed to the published version of the manuscript.