This paper proposes an optimization procedure based on eigenvalues to carry out the stabilization function of the Gate-Controlled Series Capacitor (GCSC) in a power system. It is aimed to provide a reliable damping framework by means of a GCSC based multi-objective damping controller. The proposed method employs Particle Swarm Optimization (PSO) to search for optimal parameter settings of a widely used multi-objective lead-lag damping controller. The eigenvalue analysis is considered as the cornerstone of the performed studies in order to investigate the multi-objective methodology in which the unstable or lightly damped modes are scheduled to effectively shift to some prescribed stability zones in the s-plane. The effectiveness of the suggested approach in damping local and interarea oscillations modes in a multi-machine power system, over a wide range of loading conditions, is confirmed through eigenvalue analysis and time simulation.