Hybrid Grey Wolf Optimizer with discrete prism dispersion strategy for solving flexible job-shop scheduling problem

The Flexible job-shop scheduling problem (FJSP) is a quintessential NP-hard problem in the field of production scheduling. With the development of intelligent manufacturing industry, minimizing the total completion time in workshops has become a crucial research focus. Swarm intelligence algorithms have been widely used to solve the FJSP. However, they still suffer from issues such as premature convergence and a tendency of trapping in local optimum. In addition, as iterations increase, the basic parameters of the algorithm still need to be flexibly adjusted. To address these challenges, we propose a hybrid grey wolf optimization algorithm incorporating a discrete prism dispersion strategy (HGWO-DPDS). Inspired by the optical dispersion of light through a prism, this strategy simulates a multi-directional refraction process to diversify the population and improve global exploration. First, in the position update stage, a critical-path-guided mechanism is introduced in the operation sequencing stage to identify and perturb bottleneck operations, while in the machine selection stage, machine-guided convergence enhances the search toward the current best solution. Secondly, the prism-inspired dispersion strategy expands the search directions through multiple reference centers. Finally, an adaptive mutation operator is applied to maintain population diversity and avoid stagnation. We conduct a comprehensive evaluation of the proposed model through benchmark experiments on three widely used datasets—MK, Kacem, and Lawrence instances. HGWO-DPDS is compared with several existing algorithms. The experimental results demonstrate that the proposed framework achieves near-optimal makespan values on most instances, while maintaining stable and reliable performance in solving the FJSP, particularly excelling at escaping local optima compared to existing methods.