[论文解读] Mamba Meets Scheduling: Learning to Solve Flexible Job Shop Scheduling with Efficient Sequence Modeling

Zhi Cao, Cong Zhang+3 more|arXiv (Cornell University)|Feb 25, 2026

Scheduling and Optimization Algorithms被引用 0

一句话总结

论文为灵活车间调度引入了 Mamba-CrossAttention (M-CA)，利用线性时间的 Mamba 状态空间模型实现端到端、高效的序列建模，并在 FJSP 基准测试中优于基于学习的基线方法。

ABSTRACT

The Flexible Job Shop Problem (FJSP) is a well-studied combinatorial optimization problem with extensive applications for manufacturing and production scheduling. It involves assigning jobs to various machines to optimize criteria, such as minimizing total completion time. Current learning-based methods in this domain often rely on localized feature extraction models, limiting their capacity to capture overarching dependencies spanning operations and machines. This paper introduces an innovative architecture that harnesses Mamba, a state-space model with linear computational complexity, to facilitate comprehensive sequence modeling tailored for FJSP. In contrast to prevalent graph-attention-based frameworks that are computationally intensive for FJSP, we show our model is more efficient. Specifically, the proposed model possesses an encoder and a decoder. The encoder incorporates a dual Mamba block to extract operation and machine features separately. Additionally, we introduce an efficient cross-attention decoder to learn interactive embeddings of operations and machines. Our experimental results demonstrate that our method achieves faster solving speed and surpasses the performance of state-of-the-art learning-based methods for FJSP across various benchmarks.

研究动机与目标

• 将 Mamba 模型扩展到调度领域以高效解决 FJSP。
• 提出 Mamba-CrossAttention，以从完整序列中学习交互的操作-机器嵌入。
• 用线性时间序列建模替代基于图的状态设计，以提升性能和速度。
• 在多样化的 FJSP 基准测试中展示接近最优解和最前沿结果。

提出的方法

• 编码器-解码器架构，其中编码器使用双重 Mamba 块分别提取操作和机器特征。
• 跨注意力解码器以融合操作和机器嵌入并学习交互表示。
• 决策网络将操作、机器和全局特征以及候选对特征拼接以计算选择概率。
• 将 FJSP 作为可在合适操作-机器对上进行的逐步决策的 MDP 形式，使用 makespan 为奖励。
• 使用 PPO 在演员-评论家框架中进行训练，利用 GAE 提高稳定性。
• 在六个公开 FJSP 基准测试以及合成/大规模实例上与基线方法进行对比评估。

Figure 1. Disjunctive graph representations of JSP and FJSP with 3 jobs and 3 machines. The arrows on black lines indicate precedence within jobs, while dotted lines represent disjunctive arcs, whose directions must be determined to establish a valid schedule. Disjunctive arcs of the same color indi

实验结果

研究问题

• RQ1 通过 Mamba 的全序列建模是否能改进 FJSP 表征学习，超越邻域受限的图方法？
• RQ2 Mamba-CrossAttention 架构是否能够在达到接近最优的 makespan 的同时实现更快的求解速度？
• RQ3 在标准和大规模 FJSP 实例中，M-CA 与基于图的与启发式基线相比有何表现？
• RQ4 FJSP 是否可以有效地被框架为端到端学习问题，配合编码器-解码器策略和 PPO 训练？

主要发现

• M-CA 在多个 FJSP 基准测试上实现比最先进的学习型方法更快的求解速度。
• 该方法达成接近最优的解，并优于包括图注意力和基于 MLP 的方法在内的多种基线。
• Dual Mamba 编码器提供对操作与机器序列的高效特征提取，具有线性时间复杂度。
• 跨注意力解码器实现操作与机器之间的高效交互学习，复杂度为 O(|O|·|M|)。
• 基于 PPO 的训练结合 GAE 提供稳定优化，在合成与公开基准上具有强大表现。

Figure 2. The overall architecture of our proposed Mamba-CrossAttention framework. It comprises two fundamental components: the feature extraction network and the decision-making network. At each step in the scheduling process, the feature extraction network extracts raw features of operations and m