Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.

翻译：车辆路径问题（VRP）的学习型启发式方法因减少了对手工设计规则的依赖而备受关注。然而，现有方法通常在同构任务（固定节点规模与分布）上训练和测试，导致泛化性能受限。本文研究了一个更具挑战性但更贴近实际的场景——同时兼顾VRP中节点规模与分布的泛化问题。我们提出了一种通用元学习框架，能够高效训练具备快速适应新任务能力的初始化模型。此外，我们开发了一种简洁高效的近似方法以降低训练开销。针对旅行商问题（TSP）和带容量约束的车辆路径问题（CVRP）的合成实例与标准基准实例开展的广泛实验验证了方法的有效性。代码已开源至：https://github.com/RoyalSkye/Omni-VRP。