Power system stability is of paramount importance in the context of energy sustainability. The reliable and efficient operation of power systems is crucial for supporting modern societies, economies, and the growing demand for electricity while minimizing environmental impact and increasing sustainability. Due to the insufficient effect of power system stabilizers (PSSs) on damping the inter-area mode oscillations, Flexible AC Transmission System (FACTS) devices are utilized for damping this mode and stabilizing power systems. In the present study, a novel optimization framework considering different and variable weight coefficients based on eigenvalue locations is presented, and the parameters of PSS and variable impedance devices, including static Volt-Ampere Reactive (VAR) compensator (SVC) and Thyristor-Controlled Series Compensator (TCSC) (comprising amplifying gain factor and time constants of phase-compensating blocks), are optimized in a coordinated manner using the proposed optimization framework built based on genetic algorithm (GA). Moreover, in the suggested optimization framework, the locations of FACTS devices and control signals are considered optimization parameters. Numerical results for the IEEE 69-bus power system demonstrated an effective improvement in the damping of inter-area modes utilizing the offered approach.