This paper reports on an investigation into the optimum design for a passive tuned mass damper system which takes account of soil-structure interaction. A multi-objective optimisation approach for minimising the displacement, velocity and acceleration of the structure is adopted. Three-dimensional structural models of five-, ten-and 15-storey buildings resting on soils with different shear wave velocities are used. Damper parameters are calculated using three different approaches. In the first, the damper is tuned to the fundamental frequency of the fixed-base structure; the second approach employs modified design parameters based on ASCE 7-10, and in the third the damper is optimally designed using a multi-objective genetic algorithm optimiser. The results indicate that taking the effects of soil-structure interaction into account leads to performance improvements of the damper. On the other hand, the maximum value of the displacement of soil-structure-damper system founded on soft soil reduces by a considerable extent (about 30%) using the genetic algorithm approach. Therefore the simplicity and efficiency of using the real coded genetic algorithm method in the optimal design of tuned mass dampers compared to the other two approaches is demonstrated.