Abstract Increasing demand for electrical power and expensive expansion of power systems to meet this demand leads the planners to find techno-economical solutions to overcome these challenges. Using series capacitors as reactive power compensation devices in a long transmission lines is a well-known and suitable way to face these challenges in power systems. Transmitted electrical power and the stability margin of power systems are economically improved by the proposed series devices. However, employing the series capacitors in long transmission lines causes a well-known problem in power systems as Sub Synchronous Resonance (SSR). In the present work, the mitigation of SSR is formulated as a Multi Objective Problem (MOP) in a fuzzy framework by using optimal coordinated control of Superconducting Fault Current Limiter (SFCL) and Superconducting Magnetic Energy Storage (SMES). Objective functions of MOP includes the minimization of the initial energy stored in the SMES unit, the energy loss of SFCL, the kinetic energy in generator rotor, the active power deviations in faulted bus, and the rotor speed deviations. These five objective functions are scaled by a fuzzy operator, then the scaled objective functions are aggregated by the “max-geometric mean” operator to generate the multi objective function. To solve the proposed multi-objective problem, the Hybrid Big Bang-Big Crunch (HBB-BC) as a meta-heuristic optimization algorithm is used. In order to evaluate the efficiency of the proposed algorithm, it is implemented on the IEEE First Benchmark Model (FBM) for SSR studies. According to the simulation results of the present study, the proposed algorithm is more effective in reducing the SSR problem in comparison with other algorithms.