Curriculum Learning with GNN-based Reinforcement Learning for Job Shop Scheduling

Efficiently solving the Job Shop Scheduling Problem in real-world industrial applications requires policies that are both computationally lean and topologically robust. While Reinforcement Learning has shown potential in automating dispatching rules, existing models often struggle with a scalability bottleneck caused by quadratic graph complexity or the architectural overhead of heterogeneous layers. We introduce a unified graph framework that employs feature-based homogenization to project distinct node roles into a shared latent space. This allows a standard homogeneous Graph Isomorphism Network to capture complex resource contention with linear complexity, ensuring low-latency inference for large-scale industrial applications. Our empirical results demonstrate that our framework achieves state-of-the-art performance while exhibiting consistent zero-shot generalization. We identify the job-to-machine ratio as the primary driver of policy effectiveness, rather than absolute problem size. Based on this, we propose a hypothesis of structural saturation, demonstrating that policies trained on critically congested instances ($\mathcal{J} \approx \mathcal{M}$) learn scale-invariant resolution strategies. Agents trained at this saturation point internalize invariant conflict-resolution logic, allowing them to treat massive rectangular instances as a sequential concatenation of saturated sub-problems. This approach eliminates the need for expensive scale-specific retraining and prevents overfitting to statistical shortcuts, providing a robust and efficient pathway for deploying RL solutions in dynamic production environments.

This paper proposes a novel Variational Graph-to-Scheduler (VG2S) framework for solving the Job Shop Scheduling Problem (JSSP), a critical task in manufacturing that directly impacts operational efficiency and resource utilization. Conventional Deep Reinforcement Learning (DRL) approaches often face challenges such as non-stationarity during training and limited generalization to unseen problem instances because they optimize representation learning and policy execution simultaneously. To address these issues, we introduce variational inference to the JSSP domain for the first time and derive a probabilistic objective based on the Evidence of Lower Bound (ELBO) with maximum entropy reinforcement learning. By mathematically decoupling representation learning from policy optimization, the VG2S framework enables the agent to learn robust structural representations of scheduling instances through a variational graph encoder. This approach significantly enhances training stability and robustness against hyperparameter variations. Extensive experiments demonstrate that the proposed method exhibits superior zero-shot generalization compared with state-of-the-art DRL baselines and traditional dispatching rules, particularly on large-scale and challenging benchmark instances such as DMU and SWV.

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.