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• To propose sooty-tern optimization (STO) for designing PSS parameters of multi-machine power system. • The performance of STO is evaluated using eigenvalue analysis, simulation results and performance indices. • The results are matched with other powerful optimization techniques. • Robustness is verified on hidden operating cases also under critical disturbances. This paper reports a comparative study among four bio-inspired meta-heuristic techniques i.e. Sooty-Tern Optimization (STO), Grey Wolf Optimization (GWO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) to tune the robust Power System Stabilizer (PSS) parameters of the multi-machine power system. These approaches are successfully tested on two bench-mark systems: sixteen-machine, sixty-eight-bus New England Extended Power Grid (NEEPG) and three-machine, nine-bus Western System Coordinating Council (WSCC). The efficacy of planned PSS via STO and GWO is validated by extensive non-linear simulations, eigenvalue analysis, and performance indices for numerous operating conditions under decisive perturbations, and outcomes are matched with those of GA and PSO techniques. In addition, the robustness is also tested for these algorithms. The results indicate that the PSS design using STO and GWO improves the small-signal stability and damping performance for mitigating inter-area and local area modes of low-frequency oscillations compared to GA and PSO. [ABSTRACT FROM AUTHOR]