CoRS: Fast Neural Flexible Job-Shop Scheduling via Composite Interval State Reuse

Neural approaches to the Flexible Job Shop Scheduling Problem (FJSP), particularly those based on deep reinforcement learning (DRL), have gained growing attention in recent years. However, existing methods rely on complex feature-engineered state representations (i.e., often requiring more than 20 handcrafted features) and graph-biased neural architectures. To reduce modeling complexity and advance a more generalizable framework for FJSP, we introduce ReSched, a minimalist DRL framework that rethinks both the scheduling formulation and model design. First, by revisiting the Markov Decision Process (MDP) formulation of FJSP, we condense the state space to just four essential features, eliminating historical dependencies through a subproblem-based perspective. Second, we employ Transformer blocks with dot-product attention, augmented by three lightweight but effective architectural modifications tailored to scheduling tasks. Extensive experiments show that ReSched outperforms classical dispatching rules and state-of-the-art DRL methods on FJSP. Moreover, ReSched also generalizes well to the Job Shop Scheduling Problem (JSSP) and the Flexible Flow Shop Scheduling Problem (FFSP), achieving competitive performance against neural baselines specifically designed for these variants.

Long-horizon Flexible Job-Shop Scheduling~(FJSP) presents a formidable combinatorial challenge due to complex, interdependent decisions spanning extended time horizons. While learning-based Rolling Horizon Optimization~(RHO) has emerged as a promising paradigm to accelerate solving by identifying and fixing invariant operations, its effectiveness is hindered by the structural complexity of FJSP. Existing methods often fail to capture intricate graph-structured dependencies and ignore the asymmetric costs of prediction errors, in which misclassifying critical-path operations is significantly more detrimental than misclassifying non-critical ones. Furthermore, dynamic shifts in predictive confidence during the rolling process make static pruning thresholds inadequate. To address these limitations, we propose Graph-RHO, a novel critical-path-aware graph-based RHO framework. First, we introduce a topology-aware heterogeneous graph network that encodes subproblems as operation-machine graphs with multi-relational edges, leveraging edge-feature-aware message passing to predict operation stability. Second, we incorporate a critical-path-aware mechanism that injects inductive biases during training to distinguish highly sensitive bottleneck operations from robust ones. Third, we devise an adaptive thresholding strategy that dynamically calibrates decision boundaries based on online uncertainty estimation to align model predictions with the solver's search space. Extensive experiments on standard benchmarks demonstrate that \mbox{Graph-RHO} establishes a new state of the art in solution quality and computational efficiency. Remarkably, it exhibits exceptional zero-shot generalization, reducing solve time by over 30% on large-scale instances (2000 operations) while achieving superior solution quality. Our code is available here.

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.