A low-node-density disjunctive graph model for flexible job shop scheduling

Bidirectional job-shop scheduling with graph-theoretic features: a graph attention network and proximal policy optimization approach

A novel DRL-based approach that integrates bidirectional scheduling with graph-theoretic features to effectively solve JSSP is introduced, which achieves superior performance compared to traditional heuristics and classic DRL methods, while maintaining competitive results against recent state-of-the-art approaches.

Energy-efficient flexible job shop scheduling with heterogeneous graph embedding and adaptive proximal policy optimization

Exploiting Edge Semantics in Job Shop Scheduling Problem With Heterogeneous Graph Transformers

The Job Shop Scheduling Problem (JSSP) is commonly represented as a disjunctive graph in which nodes denote operations, while edges encode technological precedence constraints and machine‐sharing conflicts. Most existing deep reinforcement learning (DRL) approaches model this graph as homogeneous by merging precedence and contention edges into a single relation type, thereby overlooking their distinct semantics. To address this limitation, we propose the Heterogeneous Graph Transformer (HGT)‐Scheduler, a reinforcement learning framework that explicitly models the JSSP as a heterogeneous graph. Unlike existing learning methods, the proposed framework employs edge‐type‐specific attention mechanisms to distinguish precedence and machine‐contention relations, enabling richer scheduling representations. The scheduling policy is optimized using Proximal Policy Optimization (PPO). The proposed framework is evaluated on the Fisher–Thompson benchmark instances. On FT06, the HGT‐Scheduler achieves an optimality gap of 8.4%, significantly outperforming both an identical architecture without edge‐type awareness () and a Graph Isomorphism Network (GIN) baseline. On the larger FT10 instance, the proposed approach demonstrates favorable scalability, although heterogeneous and homogeneous representations exhibit comparable performance under a 50,000‐step training budget. Ablation studies identify a three‐layer attention architecture as the most effective configuration. Overall, the results demonstrate that explicitly modeling edge semantics improves reinforcement learning for intelligent job shop scheduling.

Deep Reinforcement Learning for Flexible Job Shop with Multi-AGV Production Systems via Heterogeneous Graph Neural Networks

Flexible job shop scheduling with multiple automated guided vehicles (FJSP-AGV) is a challenging production scheduling problem in intelligent manufacturing, where operation sequencing, machine assignment, AGV allocation, and transportation decisions are tightly coupled. Existing exact and meta-heuristic methods can obtain high-quality solutions, but they usually require considerable computational time for large-scale instances. Meanwhile, conventional dispatching rules can make fast decisions but often fail to capture the complex interactions among operations, machines, and AGVs. To address these challenges, this paper proposes an end-to-end deep reinforcement learning framework based on heterogeneous graph neural networks for solving FJSP-AGV. Specifically, a heterogeneous graph is constructed to represent the scheduling state, where operations, machines, and AGVs are modeled as different types of nodes, and their relationships are described by operation–machine and operation–AGV arcs. Based on this representation, a heterogeneous graph neural network is developed to extract scheduling information from different production resources. In particular, a meta-path aggregation mechanism is introduced to capture the complex interaction patterns among operations, machines, and AGVs. The proximal policy optimization algorithm is then employed to train the scheduling policy in an end-to-end manner. Experimental results on public benchmark instances and real-world cases demonstrate that the proposed method outperforms composite heuristic rules and achieves a favorable balance between solution quality and computational efficiency compared with existing state-of-the-art methods. These results indicate that the proposed HGNN-DRL framework is effective for fast and intelligent scheduling decision-making in FJSP-AGV environments.

A solution method for the traveling salesman problem based on multi-scale features and dynamic optimization

As a classic NP-hard problem, the Traveling Salesman Problem (TSP) exhibits exponentially increasing complexity with node quantity, making optimal solutions difficult for large-scale instances. Traditional exact and heuristic algorithms still struggle to balance computational cost with global optimality. Recently, deep learning has enabled end-to-end sequence modeling for TSP, yet existing models face limitations in global feature modeling, cross-scale generalization, and decoding stability. To address these issues, this study proposes a multi-scale deep optimization model based on an encoder-decoder architecture. In the encoding phase, an Exponential Moving Average (EMA) mechanism enhances global spatial correlation via multi-scale feature smoothing and dynamic weighting while suppressing feature noise. In the decoding phase, a Triplet-Reasoning attention mechanism captures high-order spatial dependencies through three-branch interaction (node, edge, path), balancing local coherence with global optimization. Additionally, a dynamic sampling strategy mitigates training-inference distribution shifts to improve generalization. Experimental results on benchmark datasets show that the proposed model outperforms mainstream deep learning methods in path length and optimality gap, demonstrating superior stability and global optimality, particularly on medium and large-scale instances. This work validates the effectiveness of the multi-scale EMA and Triplet-Reasoning mechanisms, providing a new direction for deep learning-based graph optimization research.

Preference-Guided Multi-Policy Optimization for Flexible Job Shop Scheduling

PGMPO is proposed, a novel learning framework consisting of a simple but effective multi-policy modeling approach that allows a single network to represent multiple decision-makers, and a preference-driven model optimization method that effectively guides policies to learn diverse and specialized problem-solving strategies without the need for explicit reward functions.