In recent years, the occurrence of Low Frequency Oscillations (LFOs) has increased due lo the growth in size and complexity of power systems. This has strong impact on overall system and can deteriorate power system angular stability. The classical and cost effective way of preventing low-frequency oscillations in power system is to use power system stabilizers (PSSs). These controllers have been traditionally designed using classical theory such as eigenvalue/eigenvector analyses, root locus, etc., and are made of lead-lag networks. However, because the parameters of the controllers are fixed they cannot provide adequate damping over a wide range of operating conditions. The objective of this paper is to develop cost-effective control strategy that maintain the lead-lag structure of existing PSSs while optimizing the robust performance of the controller to cope with various uncertainties in the system and varying operating conditions. In this paper a method for selecting and tuning multiple power system damping controllers simultaneously by genetic algorithms (GA s) has presented. The performance of the control system is considered for different operating conditions to ensure robustness of the controllers. Robust multi objective design of the PSSs is achieved that ensures system stability by shifting the poles to the desired place in the left half s-plane.