**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 J1 optimization approach, which gives 20% weight to the peak 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 wellknown 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. Further, the stochastic analysis of the seismic signal should also be considered by developing a sensitivity analysis (e.g., a greater number of records with greater probability of occurrence and its effects on the structure must be analyzed) and reproducing synthetic accelerograms based on the damping and frequency site conditions to be used in the tuning process via WOA.

**Author Contributions:** Conceptualization, L.A.L.-V. and D.C.; methodology, L.A.L.-V. and D.C.; software, L.A.L.-V. and D.C.; validation, D.C.; formal analysis, L.A.L.-V. and D.C.; investigation, L.A.L.-V. and D.C.; resources, L.A.L.-V., D.C. and Y.V.-G.; writing—original draft preparation, D.C.; writing—review and editing, L.A.L.-V., D.C. and Y.V.-G.; visualization, L.A.L.-V., D.C. and Y.V.-G.; supervision, L.A.L.-V. and Y.V.-G. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research and publication of this study was funded by Convocatoria para el Apoyo a Proyectos de Investigación y Creación Artística en la Universidad Nacional de Colombia-Sede Medellín 2020 (grant no. 49741).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data included in this study are available upon request by contact with the corresponding author.

**Acknowledgments:** The authors wish to thank Universidad Nacional de Colombia Sede Medellín for the financial aid and support of this research.

**Conflicts of Interest:** The authors declare no conflict of interest.
