Optimizing the Permutation Flowshop Scheduling Problem with an Improved Sparrow Search Algorithm

The Sparrow Search Algorithm (SSA) is a novel optimization method inspired by sparrows’ foraging and anti-predator behavior. It mimics their exploration and exploitation strategies to find near-optimal solutions for various optimization problems. This paper presents the first application of SSA to the widely recognized Permutation Flowshop Scheduling Problem (PFSP) with the makespan criterion as the optimization target. Our study aims to assess the effectiveness and robustness of this cutting-edge metaheuristic through computational experiments and statistical analysis. The proposed SSA is a hybrid variant that incorporates the Variable Neighborhood Search (VNS) algorithm along with a Path Relinking Strategy. The effectiveness of the proposed method is evaluated through computational experiments on PFSP benchmark instances. The performance of the hybrid SSA is compared against several well-established swarm-intelligence metaheuristics, namely Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), Tuna Swarm Optimization Algorithm (TSO), Particle Swarm Optimization Algorithm (PSO), Firefly Algorithm (FA), Bat Algorithm (BA), and the Artificial Bee Colony (ABC). To ensure fair comparison, all methods are implemented within the same computational framework as the hybrid SSA. The experimental results show that the proposed hybrid SSA achieves the lowest average mean error compared with the competing methods in solving the PFSP. The results were further validated through a comprehensive non-parametric statistical analysis using Friedman, Aligned Friedman, and Quade tests, followed by post-hoc analysis with p-adjusted values, as well as Kruskal–Wallis and Wilcoxon post-hoc tests.