用期望最大化算法训练自回归模型，解决不确定的车间调度问题。
An Expectation-Maximization Algorithm-based Autoregressive Model for the Fuzzy Job Shop Scheduling Problem
- 将模糊调度建模为生成任务，通过E-M交替优化实现端到端学习。
- 无需真实标签即可训练，在多个实例上显著优于传统方法。
- 适合需要处理不确定性的智能制造场景，对工业调度有实用价值。
模糊作业车间调度问题（FJSSP）是作业车间调度问题（JSSP）的创新扩展，引入不确定性以更贴近真实制造环境，提升了应用性但大幅增加了计算复杂度。在确定性调度领域，神经组合优化（NCO）已展现出显著成效，但其在模糊调度中的应用仍较少被探索。本文旨在填补这一空白，研究利用神经网络处理模糊信息求解FJSSP的可行性，从而借助NCO进展提升模糊调度方法。为此，我们将FJSSP视为生成任务，提出基于期望最大化算法的自回归模型（EMARM）。训练时，模型在生成调度方案（E步）与调整自回归权重（M步）之间交替进行，有效克服了缺乏真实标签这一NCO框架中的普遍难题。测试结果表明，EMARM在解决FJSSP方面表现出优越性能，具备实际应用潜力。
原文摘要 · Abstract (English)
The fuzzy job shop scheduling problem (FJSSP) emerges as an innovative extension to the job shop scheduling problem (JSSP), incorporating a layer of uncertainty that aligns the problem more closely with the complexities of real-world manufacturing environments. This improvement increases the computational complexity of deriving the solution while improving its applicability. In the domain of deterministic scheduling, neural combinatorial optimization (NCO) has recently demonstrated remarkable efficacy. However, its application to the realm of fuzzy scheduling has been relatively unexplored. This paper aims to bridge this gap by investigating the feasibility of employing neural networks to assimilate and process fuzzy information for the resolution of FJSSP, thereby leveraging the advancements in NCO to enhance fuzzy scheduling methodologies. To achieve this, we approach the FJSSP as a generative task and introduce an expectation-maximization algorithm-based autoregressive model (EMARM) to address it. During training, our model alternates between generating scheduling schemes from given instances (E-step) and adjusting the autoregressive model weights based on these generated schemes (M-step). This novel methodology effectively navigates around the substantial hurdle of obtaining ground-truth labels, which is a prevalent issue in NCO frameworks. In testing, the experimental results demonstrate the superior capability of EMARM in addressing the FJSSP, showcasing its effectiveness and potential for practical applications in fuzzy scheduling.
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