This study investigates the effectiveness of the tuned mass damper inerter (TMDI) in mitigating building response, considering the soil structure interaction (SSI). Three types of models are examined: single degree of freedom (SDOF), low-rise multi-degree of freedom (MDOF), and high-rise MDOF. Additionally, the natural period of the SDOF model is varied to explore the TMDI's efficacy across different ranges. Frequency and time domain analysis are conducted under pulse-like ground motions. The H2 and genetic algorithm (GA) are used to optimize the parameters of the TMDI. In this optimization method the transfer function for displacement response is minimized. In time domain analysis we used Newmark's integration method to solve the equation of motion for all the cases considered. It is found that the optimized TMDI proves highly effective in mitigating the displacement response of the buildings, accounting for SSI. Notably, its efficiency is more pronounced when pulse period aligns closely with the buildings' natural period. In addition, a notable pattern emerges, wherein the TMDI excels in mitigating response for buildings experiencing large motion, thereby enhancing safety under severe conditions. These findings offer valuable insights into the application and optimization of the TMDI to enhance seismic performance in various buildings, while considering complex interaction with the soil.