Hybrid Grey Wolf Optimizer with Discrete Prism Dispersion Strategy for Solving Flexible Job-Shop Scheduling Problem

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 sum of total completion times in workshops has become a crucial research focus. Swarm intelligence algorithms provide common methods to solve 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 discrete prism dispersion strategy (HGWO-DPDS). 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, the convergence ability toward optimal solution is enhanced with machine optimal guidance. Secondly, the dispersion strategy is integrated to diversify the search directionsexpand through multiple reference centers. Finally, an adaptive mutation operator is applied to maintain population diversity and prevent stagnation.We conduct a comprehensive evaluation of the proposed model through benchmark experimentson on three widely used datasets, namely the MK, Kacem, and Lawrence instances. HGWO-DPDS is compared with several existing algorithms. The experimental results demonstrate that the proposed framework achieves optimal or near-optimal makespan values on most instances, while maintaining reliable performance in solving the FJSP.