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Design of an optimal controller requires optimization of multiple performance measures that are often noncommensurable and competing with each other. Design of such a controller is indeed a multi-objective optimization problem. Being a population based approach; genetic algorithm (GA) is well suited to solve multi-objective optimization problems. This paper investigates the application of GA-based multi-objective optimization technique for the design of a thyristor controlled series compensator (TCSC)-based supplementary damping controller. The design objective is to improve the power system stability with minimum control effort. The proposed technique is applied to generate Pareto set of global optimal solutions to the given multi-objective optimization problem. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. Simulation results are presented to show the effectiveness and robustness of the proposed approach.