Neural combinatorial optimization (NCO) has gained significant attention due to the potential of deep learning to efficiently solve combinatorial optimization problems. NCO has been widely applied to job shop scheduling problems (JSPs) with the current focus predominantly on deterministic problems. In this paper, we propose a novel attention-based scenario processing module (SPM) to extend NCO methods for solving stochastic JSPs. Our approach explicitly incorporates stochastic information by an attention mechanism that captures the embedding of sampled scenarios (i.e., an approximation of stochasticity). Fed with the embedding, the base neural network is intervened by the attended scenarios, which accordingly learns an effective policy under stochasticity. We also propose a training paradigm that works harmoniously with either the expected makespan or Value-at-Risk objective. Results demonstrate that our approach outperforms existing learning and non-learning methods for the flexible JSP problem with stochastic processing times on a variety of instances. In addition, our approach holds significant generalizability to varied numbers of scenarios and disparate distributions.

翻译：神经组合优化（NCO）因其利用深度学习高效解决组合优化问题的潜力而受到广泛关注。NCO已被广泛应用于作业车间调度问题（JSPs），目前的研究主要集中在确定性问题上。本文提出了一种新颖的基于注意力的场景处理模块（SPM），以扩展NCO方法用于求解随机JSPs。我们的方法通过一种注意力机制显式地整合随机信息，该机制捕获采样场景（即随机性的近似）的嵌入表示。基于此嵌入表示，基础神经网络受到所关注场景的干预，从而学习在随机性下的有效策略。我们还提出了一种训练范式，该范式可与期望完工时间或风险价值目标函数协同工作。实验结果表明，在多种实例上，针对具有随机处理时间的柔性JSP问题，我们的方法优于现有的学习和非学习方法。此外，我们的方法对于不同数量的场景和不同的分布具有显著的泛化能力。