To accomplish an appropriate performance of tuned mass dampers (TMDs) in building structures subjected to earthquake excitations, considerable amounts of mass must be added at upper floors, which in occasions may result impractical or economically unfeasible, especially in tall buildings. Therefore, this investigation contemplates two possible alternatives for the passive control of buildings avoiding the addition of large masses through inerter-based devices, the Tuned Mass Damper Inerter (TMDI), and a variant-type of Tuned Inerter Damper (TID) proposed herein. The former couples the classic TMD with an inerter, a two-terminal mechanical device able to produce a force proportional to the relative acceleration between its terminals, acting as a TMD mass amplifier. The latter is based on the conventional TID scheme, with the main difference that its location is changed from the ground story-level to the last two levels of the structural system. A metaheuristic optimization algorithm based on the differential evolution method is used to solve the tuning problem of the control devices. Besides, eight different accelerograms of recorded earthquakes are considered to simulate the seismic loads during the optimization process, in which the mitigation of the seismic response is measured by the reduction of three objective functions: horizontal peak displacements, root mean square (RMS) response of displacements, and horizontal peak floor acceleration. Three case-studies are employed for the analysis, determined from actual buildings of Medellin city from low, medium to high rise (30 meters, 97 meters, and 144 meters respectively). In the TMDI analysis, the results show a clear trend in the amplification of displacements as inertance values increase, and consequently, a better behavior of the case-studies controlled via TMD is attained. On the contrary, the numerical results exhibited a clear enhancement of the seismic performance of the case-studies when the variant-type of the TID proposed herein is applied, better than conventional TIDs installed at the ground story level.