This thesis proposes an optimization procedure to achieve the best configuration of multiple degrees of freedom tuned mass dampers (TMD) to mitigate the global dynamic aeroelastic response of aerospace structures. The TMD design parameters are investigated in terms of their individual mass, stiffness, damping, and location on the target structure. In order to determine the optimum sets of TMD, a multi-objective design optimization employing a genetic algorithm is implemented, where the selected fitness functions for the analysis are the minimization of the total mass included with the resonators and concurrent minimization of the peak displacement at specific structural nodes. Two case studies are presented, where the method is tested to minimize the pointing error of large Earth-based radio antennas. Fourteen operational scenarios of wind gust are considered, employing two models of atmospheric disturbances, where the dynamic aeroelastic response of the structure is analyzed in the frequency and the time domains.