Districting is a complex combinatorial problem that consists in partitioning a geographical area into small districts. In logistics, it is a major strategic decision determining operating costs for several years. Solving districting problems using traditional methods is intractable even for small geographical areas and existing heuristics often provide sub-optimal results. We present a structured learning approach to find high-quality solutions to real-world districting problems in a few minutes. It is based on integrating a combinatorial optimization layer, the capacitated minimum spanning tree problem, into a graph neural network architecture. To train this pipeline in a decision-aware fashion, we show how to construct target solutions embedded in a suitable space and learn from target solutions. Experiments show that our approach outperforms existing methods as it can significantly reduce costs on real-world cities.

翻译：分区是一种复杂的组合优化问题，其核心在于将地理区域划分为若干小型区域。在物流领域，分区是一项重大的战略决策，将决定未来数年的运营成本。即使对于小型地理区域，采用传统方法解决分区问题也极为困难，而现有启发式方法往往只能提供次优解。本文提出一种结构化学习方法，可在数分钟内为现实世界的分区问题找到高质量解。该方法基于将组合优化层——带容量约束的最小生成树问题——集成至图神经网络架构中。为以决策感知的方式训练该流程，我们阐述了如何构建嵌入于适宜空间的目标解，并实现从目标解中学习。实验表明，本方法优于现有技术，能够在实际城市案例中显著降低分区成本。