TL;DR
This paper introduces RsGCN, a novel subgraph-based rescaling method for GCNs that significantly improves the generalization and reduces training costs for solving large-scale TSPs, enabling effective transfer from small to very large instances.
Contribution
The paper proposes RsGCN, a scale-normalization technique for GCNs, combined with a reconstruction-based search, to enhance cross-scale generalization and efficiency in TSP solving.
Findings
RsGCN generalizes from small to large TSP instances without fine-tuning.
Achieves high accuracy on instances up to 10,000 nodes with minimal training.
Outperforms existing neural methods in parameter efficiency and training speed.
Abstract
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…
Peer Reviews
Decision·Submitted to ICLR 2026
- Simple but effective: The core idea of the RsGCN model is refreshingly straightforward. The authors correctly identify that as TSP instances grow, the nodes in the unit square get denser, and the average edge lengths shrink. GCNs, being sensitive to the distribution of their input features (edge weights), fail to generalize. The solution of subgraph-based rescaling isn't a massive new architecture, a complex attention mechanism, or a heavy generative decoder. - Exceptional training efficiency
- Limited contributions on the scope of studied problems. Only tsp is evaluated. More problems e.g. cvrp should be included to demonstrate the effectiveness. - RBS vs. Classical Heuristics: The RBS algorithm is a sophisticated, multi-stage local search (destroy, repair, 2-opt, adaptive weighting). It is a strong heuristic in its own right, which is good, but it also means the performance lift is not purely from the learned GCN. Table 1 shows that RBS (using 5-NN, no GCN) is already a top-tier
1. The proposed method incurs low training costs and, according to experimental results, delivers good performance and generalization. 2. The paper conducts a thorough ablation study on the use of edge normalization and node K-NN.
1. Clearly, the sole focus on TSP is a major limitation of this paper. The proposed ``RsGCN+RBS`` is an improved variant of the earlier ``Att-GCN+MCTS`` pipeline. The latter, over the past few years, has not demonstrated any clear trend toward being extended to other combinatorial problems. 2. The authors do not report the results right after ``STATE INITIALIZATION``. Similar to ``Att-GCN``, the performance gains may largely come from the post-processing steps. The underlying idea of these post
1. Subgraph-based edge normalization effectively eliminates scale-dependent distortions, enabling robust zero-shot generalization. 2. Training on mixed-scale instances (≤100 nodes) for only 3 epochs suffices for 10K-node generalization. 3. RsGCN uses the fewest parameters among neural baselines (416K parameters vs. 1.4M–11M) and scales linearly in inference. 4. Outperforms GCN/Transformer baselines on both synthetic and real-world TSPs.
1. The idea of using k-NN to prune a neural architecture is not really novel, although it is suitable to solving TSP problems. 2. The idea of reconstruction-based search is not really novel either, similar to the improvement-based solvers introduced before.
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