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

2026-04-11

AI Summary

This work addresses the efficiency and solution quality bottlenecks in long-horizon flexible job shop scheduling, which arise from structural complexity and misidentification of critical paths. To this end, the authors propose the Graph-RHO framework, which models subproblems via an operation-machine heterogeneous graph network and integrates a critical-path-aware mechanism with an adaptive thresholding strategy based on uncertainty estimation. Within a rolling optimization scheme, the method dynamically identifies and fixes stable operations. Key innovations include a topology-aware heterogeneous graph neural network, critical-path-guided training bias, and dynamic calibration of decision boundaries. Experimental results demonstrate that the approach achieves new state-of-the-art performance on standard benchmarks, exhibits strong zero-shot generalization, and reduces solving time by over 30% while yielding higher-quality solutions on large-scale instances with up to 2,000 operations.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Intelligent Robots: Learning & Optimization for ROB
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work

Abstract

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 \href{https://github.com/IntelliSensing/Graph-RHO}{here}.

Problem

• Flexible Job-Shop Scheduling
• Rolling Horizon Optimization
• Critical Path
• Heterogeneous Graph Network
• Long-Horizon Scheduling

Innovation

• heterogeneous graph network
• critical-path awareness
• rolling horizon optimization
• adaptive thresholding
• zero-shot generalization