AI 中文总结
该研究针对柔性作业车间调度中深度强化学习模型参数多、推理慢的问题，提出PLAN框架，通过解耦状态演化与上下文聚合实现高效学习，在三类基准任务上优于基线，参数量仅为基线的22%-47%且延迟显著降低。
AI 中文摘要
深度强化学习（DRL）用于柔性作业车间调度（FJSP）的方法，高度依赖以注意力为核心的架构来实现最先进的性能。然而，随着问题规模扩大，这些模型存在参数数量过多、推理延迟过高的问题。类液体神经网络（LNN）是一种参数高效的自适应状态演化建模替代方案，但其固有的顺序动态会造成计算效率瓶颈。为解决这一权衡问题，我们提出PLAN（Parallel Liquid-inspired Approximation Network，并行类液体近似网络），这是一种轻量级表示学习框架，将连续的类液体状态动力学重新表述为可离散化且可并行化的形式。PLAN在结构上将状态演化与上下文聚合解耦：类液体更新负责处理主要的演化状态表示，轻量级上下文聚合模块提供互补的全局上下文。此外，PLAN作为通用即插即用主干，可泛化到复杂的FJSP变体，与紧凑随机模块配对用于随机FJSP，在多方面动态FJSP中可替代沉重的异构图变换器。在确定性、随机性和多方面动态FJSP基准上的广泛评估表明，与对应的最先进基线相比，PLAN分别将平均完工时间（makespan）降低了1.2%、1.4%和2.3%，在某一基准设置中改进达到10.2%；同时，PLAN分别将平均推理延迟降低了13.2%、31.7%和26.9%，在最大规模实例上的最大降低幅度达69.2%，且仅使用基线模型22%-47%的参数。
英文摘要
Deep reinforcement learning (DRL) approaches for flexible job shop scheduling (FJSP) heavily rely on attention-centric architectures to achieve state-of-the-art performance. However, these models suffer from excessive parameter counts and prohibitive inference latency as problem scales expand. While liquid neural networks (LNNs) offer a parameter-efficient alternative for modeling adaptive state evolution, their inherently sequential dynamics bottleneck computational efficiency. To resolve this trade-off, we propose PLAN (Parallel Liquid-inspired Approximation Network), a lightweight representation learning framework that reformulates continuous liquid-state dynamics into a discretized and parallelizable formulation. PLAN structurally decouples state evolution from context aggregation, where liquid-inspired updates handle the primary evolving state representation, and a lightweight context aggregation module provides complementary global context. Furthermore, PLAN acts as a versatile, plug-and-play backbone that generalizes to complex FJSP variants, pairing with a compact stochastic module for stochastic FJSP and replacing heavy heterogeneous graph transformers in multi-faceted dynamic FJSP. Extensive evaluations across deterministic, stochastic, and multi-faceted dynamic FJSP benchmarks show that PLAN reduces the average makespan by 1.2%, 1.4%, and 2.3%, respectively, compared with the corresponding state-of-the-art baselines, with the improvement reaching 10.2% in one benchmark setting. PLAN also reduces average inference latency by 13.2%, 31.7%, and 26.9%, respectively, with a maximum reduction of 69.2% on the largest instances, while using only 22$-$47% of the baseline parameters.
