The study on the performance of the nonlinear friction tuned mass dampers (FTMD) for the mitigation of the seismic responses of the structures is a topic that still inspires the efforts of researchers. The present paper aims to carry out a numerical study on the optimum tuning of TMD and FTMD parameters using a multi-objective particle swarm optimization (MOPSO) algorithm including soil-structure interaction (SSI) effects for seismic applications. Considering a 3-story structure, the performances of the optimized TMD and FTMD are compared with the uncontrolled structure for three types of soils and the fixed base state. The simulation results indicate that, unlike TMDs, optimum tuning of FTMD parameters for a large preselected mass ratio may not provide a best and optimum design. For low mass ratios, optimal selection of friction coefficient has an important key to enhance the performance of FTMDs. Consequently, a free parameter search of all FTMD parameters provides a better performance in comparison with considering a preselected mass ratio for FTMD in the optimum design stage of the FTMD. Furthermore, the SSI significant effects on the optimum design of the TMD and FTMD. The simulation results also show that the FTMD provides a better performance in reducing the maximum top floor displacement and acceleration of the building in different soil types. Moreover, the performance of the TMD and FTMD decrease with increasing soil softness, so that ignoring the SSI effects in the design process may give an incorrect and unrealistic estimation of their performance.