Abstract
Abstract
This paper proposes a hybrid genetic algorithm with variable neighborhood search (HGVNSA) for the flexible job-shop scheduling problem (FJSP). The algorithm adopts a genetic algorithm as the global search framework, using three-layer encoding and active decoding. Population initialization combines global selection, local selection, and random selection strategies. The genetic operations introduce path-relinking crossover and adaptive mutation to enhance exploration. On this basis, a critical-path-based double-neighborhood variable neighborhood search (VNS) is embedded: the N8 neighborhood optimizes the sequence of operations on the same machine, while the k‑insertion neighborhood reallocates operations across machines, jointly improving local exploitation. Experiments on the Brandimarte MK benchmark instances show that HGVNSA steadily reaches the known optimal solutions in 6 out of 10 cases, outperforming HGWO, HLO-PSO, HA, and other comparison algorithms. Ablation studies verify the effectiveness of each mechanism. In a real-world case of gear shaft processing at Company A, the algorithm improves production efficiency by 8.81% over the traditional genetic algorithm, confirming its engineering value. This study provides an efficient and robust solution for FJSP, with future extensions to distributed scheduling and deep reinforcement learning guided neighborhood selection.