Network flow problems, which involve distributing traffic over a network such that the underlying infrastructure is used effectively, are ubiquitous in transportation and logistics. Among them, the Multi-Commodity Network Flow (MCNF) problem is of general interest, as it concerns the distribution of multiple flows of different sizes between several sources and sinks, while achieving effective utilization of the links. Due to the appeal of data-driven optimization, these problems have increasingly been approached using graph learning methods. In this paper, we propose a novel graph learning architecture for network flow problems called Per-Edge Weights (PEW). This method builds on a Graph Attention Network and uses distinctly parametrized message functions along each link. We extensively evaluate the proposed solution through an Internet flow routing case study using $17$ Service Provider topologies and $2$ routing schemes. We show that PEW yields substantial gains over architectures whose global message function constrains the routing unnecessarily. We also find that an MLP is competitive with other standard architectures. Furthermore, we shed some light on the relationship between graph structure and predictive performance for data-driven routing of flows, an aspect that has not been considered by existing work in the area.

翻译：网络流问题涉及在网络上分配流量，以有效利用底层基础设施，在交通运输和物流领域普遍存在。其中，多商品网络流（MCNF）问题引起普遍关注，因为它涉及在多个源节点和汇节点之间分配不同规模的多种流量，同时实现链路的高效利用。受数据驱动优化方法的吸引，这些问题越来越多地采用图学习方法来解决。本文针对网络流问题提出一种新型图学习架构，称为逐边权重法（PEW）。该方法基于图注意力网络，沿每条链路使用不同参数化的消息函数。我们通过一个互联网流路由案例研究，使用17个服务提供商拓扑结构和2种路由方案，对所提方案进行了广泛评估。结果表明，PEW相比那些使用全局消息函数不必要地约束路由的架构取得了显著增益。同时，我们发现多层感知机（MLP）与其他标准架构相比具有竞争力。此外，本文揭示了图结构与数据驱动流路由预测性能之间的关系，这是该领域现有工作尚未考虑的一个方面。