Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. Yet, existing methods are unsuitable for routing on multigraphs, which feature multiple edges with distinct attributes between node pairs, despite their strong relevance in real-world scenarios. In this paper, we propose two graph neural network-based methods to address multi-objective routing on multigraphs. Our first approach operates directly on the multigraph by autoregressively selecting edges until a tour is completed. The second model, which is more scalable, first simplifies the multigraph via a learned pruning strategy and then performs autoregressive routing on the resulting simple graph. We evaluate both models empirically, across a wide range of problems and graph distributions, and demonstrate their competitive performance compared to strong heuristics and neural baselines.

翻译：近年来，基于学习的路由方法在单目标和多目标场景中均获得了广泛关注。然而，现有方法无法适用于多图上的路由问题，尽管多图（即节点对之间存在多条具有不同属性的边）在现实场景中具有重要应用价值。本文提出两种基于图神经网络的方法来解决多图上的多目标路由问题。第一种方法直接在多图上运行，通过自回归方式选择边直至完成路径遍历。第二种更具可扩展性的模型，首先通过习得的剪枝策略对多图进行简化，随后在得到的简单图上执行自回归路由。我们在多样化问题与图分布上对两种模型进行了实证评估，结果表明相较于强启发式方法与神经基线模型，所提方法均展现出具有竞争力的性能。