This paper analyzes the integration of artificial intelligence (AI) with mixed integer linear programming (MILP) to address complex optimization challenges in air transportation with explainability. The study aims to validate the use of Graph Neural Networks (GNNs) for extracting structural feature embeddings from MILP instances, using the air05 crew scheduling problem. The MILP instance was transformed into a heterogeneous bipartite graph to model relationships between variables and constraints. Two neural architectures, Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT) were trained to generate node embeddings. These representations were evaluated using Instance Space Analysis (ISA) through linear (PCA) and non-linear (UMAP, t-SNE) dimensionality reduction techniques. Analysis revealed that PCA failed to distinguish cluster structures, necessitating non-linear reductions to visualize the embedding topology. The GCN architecture demonstrated superior performance, capturing global topology with well-defined clusters for both variables and constraints. In contrast, the GAT model failed to organize the constraint space. The findings confirm that simpler graph architectures can effectively map the sparse topology of aviation logistics problems without manual feature engineering, contributing to explainability of instance complexity. This structural awareness provides a validated foundation for developing future Learning to Optimize (L2O) agents capable of improving solver performance in safety-critical environments.

翻译：本文分析了人工智能（AI）与混合整数线性规划（MILP）的融合，以解决航空运输中具有可解释性的复杂优化挑战。研究旨在验证使用图神经网络（GNNs）从MILP实例中提取结构特征嵌入的方法，以air05机组调度问题为例。MILP实例被转换为异质二分图，以建模变量与约束之间的关系。训练了两种神经架构——图卷积网络（GCN）和图注意力网络（GAT）以生成节点嵌入。通过线性（PCA）和非线性（UMAP、t-SNE）降维技术，利用实例空间分析（ISA）对这些表示进行评估。分析表明，PCA无法区分聚类结构，需要非线性降维来可视化嵌入拓扑。GCN架构表现出优越性能，能够捕捉全局拓扑，并为变量和约束形成清晰的聚类。相比之下，GAT模型未能有效组织约束空间。研究结果证实，较简单的图架构能够有效映射航空物流问题的稀疏拓扑，无需手动特征工程，有助于解释实例复杂性。这种结构感知为开发未来学习优化（L2O）智能体提供了验证基础，这些智能体能够在安全关键环境中提升求解器性能。