## 1 Introduction
Based on the foregoing discussion, Table 1 provides a concise comparison of the main categories of FJSP solution methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Method Category** & **Advantages** & **Disadvantages** \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Exact \\ Methods \\ \end{tabular} } & Mathematical Programming/ & (1) Precise modeling & (1) High computational complexity \\  & Constraint Programming et al. & (2) Theoretically optimal solutions & (2) Long computation time for large-scale problems \\  & Rule-Based Heuristics & (1) Low computational cost & (1) Local optimization \\  & & (2) Simple implementation & (2) Poor solution quality \\  & Intelligent Optimization & (1) Near-optimal solutions & (1) High complexity \\  & Algorithms & (1) Adaptable to dynamic environments & (1) Limited scalability for varying complexity \\  & CNN/MLP-Based DRL & (1) Captures topological dependencies & (2) Ignores node relationships \\  & GNN-Based DRL & (1) Captures topological dependencies & (1) Oversimplified node heterogeneity handling \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of existing methods. Although researchers have made significant progress in solving FJSPs using deep reinforcement learning methods, existing approaches often rely on static feature descriptions of the scheduling process, failing to effectively exploit and utilize the frequently changing task and resource state features during scheduling [32]. This may lead to delays and inaccuracies in scheduling decisions. Additionally, when facing FJSPs of different scales and complexities, existing strategies often lack flexibility, and the adaptability and optimization capabilities of scheduling policies remain insufficient to ensure quality and efficiency across various production scales [33]. To address the issues, this paper introduces an end-to-end deep reinforcement learning approach based on graph neural networks (GNNs) for efficiently solving the FJSP through learning high-quality scheduling policies. Initially, a heterogeneous enhanced disjunctive graph (HEDG) structure is proposed to represent the MDP states involved in solving the FJSP. A GNN-based architecture is subsequently designed to learn node embedding features, thereby effectively capturing the complex interactions and dependencies between operations as well as between operations and machines. This enables the provision of richer state information for subsequent scheduling decisions. Furthermore, a composite decision action that integrates both operation selection and machine assignment is proposed. Utilizing the PPO algorithm, the policy network is designed and trained to adaptively output optimal actions based on the current scheduling state, thereby achieving effective optimization of the flexible job shop scheduling scheme. Finally, the proposed method is validated through a case study in an aerospace structural component processing workshop, demonstrating its effectiveness across instances of varying scales. The main contributions of this study are as follows:  
1. This study introduces the HEDG structure for modeling the FJSP. The HEDG captures both the precedence constraints and the compatibility between operations and machines, enabling dynamic, real-time updates of scheduling states. This dynamic feature enhances traditional static models, making the framework adaptable to changing production environments and real-time scheduling decisions. 2. A heterogeneous enhanced graph neural network (HEGNN) architecture is proposed to extract rich feature representations from the HEDG. By effectively capturing the complex interactions and dependencies between operations and machines, the HEGNN enhances the feature representation, providing deep insights into the scheduling state. This leads to improved decision-making for both operation assignment and machine selection. 3. The integration of HEGNN with the PPO algorithm allows for joint optimization of both operation assignment and machine selection.