## 5 Conclusions  
In this study, a methodology for the selection of optimal design parameters for TMDs based on WOA to reduce the dynamic response of buildings subjected to seismic excitations was presented. Six different objective functions were proposed to be minimized in the WOA methodology. These functions were related to the reduction of the maximum horizontal peak displacement of the structure, the RMS response of displacements, and four more weighted linear combinations of the same parameters. The proposed methodology was applied to a 32-story case-study derived from an actual building structure, and subjected to different ground motion records. According to the analysis on the dynamic history of displacements of the structure, it may be concluded that the J\({}_{1}\) optimization approach, which gives 20% weight to the peak \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**TMD \(\mu\) = 2\%**} \\ \hline \multicolumn{6}{c}{**Max. Displacement**} & \multicolumn{4}{c}{**RMS Displacement**} \\ \hline Uncontrolled (m) & Controlled (m) & PI & Uncontrolled (m) & Controlled (m) & PI \\ \hline
0.7213 & 0.7047 & 0.9770 & 0.1569 & 0.1319 & 0.8406 \\ \hline \multicolumn{6}{c}{**TMD \(\mu\) = 5\%**} \\ \hline Uncontrolled (m) & Controlled (m) & PI & Uncontrolled (m) & Controlled (m) & PI \\ \hline
0.7213 & 0.6781 & 0.9401 & 0.1569 & 0.1100 & 0.7013 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Response parameters for the 32 nd story of the structure subjected to Petrolia earthquake. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**TMD \(\mu\) = 2\%**} \\ \hline \multicolumn{6}{c}{**Max. Displacement**} & \multicolumn{4}{c}{**RMS Displacement**} \\ \hline Uncontrolled (m) & Controlled (m) & PI & Uncontrolled (m) & Controlled (m) & PI \\ \hline
0.3231 & 0.3225 & 0.9980 & 0.0839 & 0.0701 & 0.8354 \\ \hline \multicolumn{6}{c}{**TMD \(\mu\) = 5\%**} \\ \hline Uncontrolled (m) & Controlled (m) & PI & Uncontrolled (m) & Controlled (m) & PI \\ \hline
0.3231 & 0.3158 & 0.9772 & 0.0839 & 0.0630 & 0.7513 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Response parameters for the 32 nd story of the structure subjected to San Fernando earthquake. floor displacements and 80% weight to the RMS response of displacements, led to the best reductions in the transient response within both evaluated parameters, although a good performance was also exhibited using OA2 and J2 optimization approaches. Furthermore, a weighted procedure for determining an average design set of parameters for TMDs was explored. The methodology, proposed originally for base isolation systems, was adapted for the tuning of linear mass dampers, showing promising results that can be improved in forthcoming investigations by considering a large number of records in the tuning process. The proposed technique for obtaining design parameters of TMDs based on WOA is demonstrated to be successful, fast, and reliable by achieving percentages of reduction in the maximum floor displacement of up to 43% and RMS values of displacement of up to 52%. The results of this research highlighted the advantages of the WOA over other well-known metaheuristics, such as DEM and other bio-inspired algorithms. The proposed technique exhibited less computational cost, avoiding operations like mutation or crossover, and reductions in the processing time up to 45% were observed. Finally, to perform a realistic tuning of TMDs through WOA, a more comprehensive analysis is required. Future works should take into account inter-story drifts and floor accelerations which are directly associated with the structural damage, as well as consider the nonlinear properties of the structural system.