# Graph-RHO: Critical-path-aware Heterogeneous Graph Network for Long-Horizon Flexible Job-Shop Scheduling

arXiv: https://arxiv.org/abs/2604.10073 · HTML: https://mlsanity.com/paper/2604.10073/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 11 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Flexible Job Shop Scheduling via Dual Attention Network Based Reinforcement Learning](https://mlsanity.com/paper/2305.05119/) (2023)
- [Residual Scheduling: A New Reinforcement Learning Approach to Solving Job Shop Scheduling Problem](https://mlsanity.com/paper/2309.15517/) (2023)
- [Learning-Guided Rolling Horizon Optimization for Long-Horizon Flexible Job-Shop Scheduling](https://mlsanity.com/paper/2502.15791/) (2025)
- [Learning to Branch in Combinatorial Optimization with Graph Pointer Networks](https://mlsanity.com/paper/2307.01434/) (2023)

## Abstract (arXiv)

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 mboxGraph-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 hrefhttps://github.com/IntelliSensing/Graph-RHOhere.