This study investigates the efficacy of the Grey Wolf Optimizer (GWO), a newer Swarm Intelligence (SI) algorithm, in addressing the Permutation Flowshop Scheduling Problem (PFSP). A hybrid approach integrating GWO with Variable Neighborhood Search (VNS) and Path Relinking strategies is proposed to enhance scheduling optimization in industrial settings. Emphasizing the importance of initial population quality in SI algorithms, a randomized NEH (Nawaz-Enscore-Ham) method is advocated for generating high-quality initial points for GWO. Through a comprehensive comparative study involving prominent SI algorithms such as Particle Swarm Optimization (PSO), Firefly Algorithm (FA), Bat Algorithm (BA), and Artificial Bee Colony (ABC), GWO’s performance is evaluated using statistical analyses including Friedmans Test, Friedmans Aligned Test, and Quade Test. The findings reveal GWO’s satisfactory results, positioning it as a promising contender for PFSP optimization. The study underscores the significance of hybridization techniques and statistical analyses in driving improvements in operational efficiency and performance in industrial scheduling applications.