arXiv:2506.00533cs.LGcs.NE2025-06

通过子图重缩放提升GCN在旅行商问题上的泛化能力,训练成本更低。

RsGCN: Subgraph-Based Rescaling Enhances Generalization of GCNs for Solving Traveling Salesman Problems

  • 用子图重缩放统一处理不同规模的边长,学习跨尺度特征
  • 仅用3轮训练即可在100节点数据上泛化到1万节点问题
  • 适合需要低训练成本和强泛化的图神经网络求解器研究者

基于GCN的旅行商问题(TSP)求解器面临两大挑战:跨尺度泛化能力差与高训练成本。为此,我们提出子图重缩放图卷积网络(RsGCN)。针对与问题规模相关的节点与边特征,设计子图重缩放以归一化子图边长。在统一子图视角下,RsGCN可低成本高效学习小规模TSP的通用表示。为利用并评估RsGCN生成的热图,设计基于重构的搜索(RBS),引入自适应权重重构过程以避免局部最优。结合RsGCN与RBS的架构,求解器实现优异泛化与低训练成本:仅在包含最多100个节点的混合规模数据集上训练3轮,即可无需微调地推广至10,000节点实例。大量实验表明,其在20至10,000节点的9种均匀分布实例及TSPLIB的78个真实世界实例上表现领先,且所需可学习参数和训练轮次均少于其他神经网络竞争者。

原文摘要 · Abstract (English)

GCN-based traveling salesman problem (TSP) solvers face two critical challenges: poor cross-scale generalization for TSPs and high training costs. To address these challenges, we propose a Subgraph-Based Rescaling Graph Convolutional Network (RsGCN). Focusing on the scale-dependent features (i.e., features varied with problem scales) related to nodes and edges, we design the subgraph-based rescaling to normalize edge lengths of subgraphs. Under a unified subgraph perspective, RsGCN can efficiently learn scale-generalizable representations from small-scale TSPs at low cost. To exploit and assess the heatmaps generated by RsGCN, we design a Reconstruction-Based Search (RBS), in which a reconstruction process based on adaptive weight is incorporated to help avoid local optima. Based on a combined architecture of RsGCN and RBS, our solver achieves remarkable generalization and low training cost: with only 3 epochs of training on a mixed-scale dataset containing instances with up to 100 nodes, it can be generalized successfully to 10K-node instances without any fine-tuning. Extensive experiments demonstrate our advanced performance across uniform-distribution instances of 9 different scales from 20 to 10K nodes and 78 real-world instances from TSPLIB, while requiring the fewest learnable parameters and training epochs among neural competitors.

图神经网络旅行商问题泛化能力低训练成本

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