Ground motion-induced vibrations in buildings can affect the integrity of these systems in dangerous ways due to the lateral displacements and interstory drift magnitudes, triggering different damage mechanisms. In recent years, the use and study of different structural control devices that allow dissipating the input energy of structural systems in a simple, efficient, and safe way have been increasing. Thus, the implementation of the inerter as a complementary mechanism in a wide variety of passive control devices has proven to be an effective option for the protection of civil structures. This paper explores the numerical implementation of a Tuned Inerter Damper (TID) for the reduction of lateral displacements and interstory drift in a shear frame building subjected to different ground motions. For this purpose, the optimal design parameters of the device have been obtained using an optimization process based on an evolutionary cultural algorithm whose objective function is a weighted linear combination of the peak displacement and the maximum interstory drift of the structure. The results obtained show significant reductions in the structural response of the system analyzed, validating the potential of TIDs as suitable tools for building control.