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The effectiveness of the tuned mass damper inerter (TMDI) in reducing the vibration of building structures under site-specific earthquake excitation is investigated. The site is Guwahati, Assam, which lies in the most severe seismic intensity zone in India. In this paper, the optimization of the TMDI design parameters is carried out for the site-specific input derived for the building site by a modulated Clough-Penzien (C-P) spectrum fitted to the power spectral density function obtained from a strong motion model of the site. All possible topologies of the TMDI, with one terminal of the inerter being connected to the damper mass attached to the top storey of the example buildings, and the other terminal being connected to any other floor, are investigated. The structure-TMDI system is analyzed both in the frequency-domain and in the time-domain. A numerical study is conducted with two example building structures. Optimization of design parameters of the TMDI is carried out using the technique of simulated annealing in the frequency-domain using the site-specific modulated Clough-Penzien spectrum as input. The performance of the optimal TMDI cases is evaluated by subjecting the example structures to 10 site-specific synthetically generated accelerograms. Results indicate that the TMDI is superior to the TMD for all topologies of the TMDI in case of the 3-storieed structure; and for topologies of the TMDI in which the inerter spans more than 4 floors for the 8-storied structure, with improved reductions in top-floor displacement, acceleration, and stroke length. [ABSTRACT FROM AUTHOR]