In this study, the robust optimum design of a recently developed passive control device, i.e., tuned mass damper inerter (TMDI) is investigated to control a 10-story base-excited shear building benchmark. The H2 and H∞ of three different objective functions (i.e., minimizing roof displacement, minimizing 7th-story displacement, and maximizing the TMD stroke) are selected as objective functions for two different single and double inerter configurations. Optimum free vibration parameters of the TMDI (i.e., natural frequency and damping ratios) are calculated using a metaheuristic technique for two different structural damping values. Additionally, the performance of the optimum designed damper and its robustness under 25 far-fault (FF) ground motions are assessed in the time domain with 12 different performance criteria (i.e., the mean and standard deviation of the maximum and norm of response histories for roof displacement, roof acceleration, and the total kinetic energy of the building). Based on current work, the best performance index for single TMDI for all three objective functions is the roof absolute acceleration, showing a maximum of 45% reduction in the mean maximum roof acceleration for 25 earthquake records. Therefore, the TMDI is most effective when the goal is to reduce the floor accelerations. The double inerter configuration shows approximately the same values for the performance indices for all three objective functions and demonstrates similar reduction for a single TMDI. However, it increases the robustness of the control method by adding redundancy and enhancing the performance for different combinations of inertance and mass ratios.
