发表机构
University of Twente（特文特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出用MILP生成的训练数据训练Transformer模型，将非置换流水车间调度转化为下一个token预测任务，实验表明其解质量优于GA、NEH启发式和随机搜索，仅弱于MILP和IG启发式，为调度研究提供新方向。
AI 中文摘要
机器学习（ML）的进展为补充传统运筹学（OR）方法创造了新机遇。Transformer模型可通过将token映射到高维嵌入空间、经注意力机制传播上下文信息，捕获token序列中的复杂交互，因此可作为非置换流水车间调度（含辅助资源）的建模候选，将其转化为下一个token预测任务，其中token代表“工件-机器-辅助资源”三元组。训练时，将混合整数线性规划（MILP）生成的调度方案进行token化，用作下一个token预测数据；推理时，随机生成部分token序列（前缀），训练后的Transformer通过约束解码完成序列。计算实验针对含8个工件、4台机器、3种辅助资源的流水车间开展，工件来自20个固定工件池，训练时采样、前缀补全时作为候选。实验结果显示，与遗传算法（GA）、NEH启发式算法、随机搜索相比，Transformer的解质量更优（总完工时间更小），仅在性能上弱于MILP模型和迭代贪心（IG）启发式算法。该研究得出结论：Transformer模型可在一定程度上从MILP优化的非置换流水车间调度中学习模式，基于Transformer的调度是未来研究的有趣方向，尤其适用于工件集固定且重复的场景。
英文摘要
Advances in machine learning (ML) have created new opportunities to complement traditional operations research (OR) methods. In particular, transformer models can capture complex interactions in token sequences by mapping tokens into a high-dimensional embedding space and propagating contextual information via attention. This makes them a candidate to model non-permutation flow shop scheduling with secondary resources as a next-token prediction task, where tokens represent job-machine-secondary resource tuples. For training, mixed-integer linear programming (MILP)-generated schedules are tokenized and used as next-token prediction data. During inference, partial token sequences (prefixes) are randomly generated and completed by the trained transformer through constrained decoding. A computational study is conducted on a flow shop with 8 jobs, 4 machines, and 3 secondary resources, where jobs are selected from a fixed pool of 20 jobs that is sampled during training and provides the candidates during prefix completion. The transformer achieves better solution quality (smaller makespans) compared to a genetic algorithm (GA), the NEH heuristic, and random search. It is outperformed only by the MILP model and the iterated greedy (IG) heuristic. The study concludes that transformer models can, to some extent, learn patterns from MILP-optimized non-permutation flow shop schedules and that transformer-based scheduling represents an interesting direction for future research, particularly in settings with a fixed, recurring job set.
