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

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.