GES-TSP: Graph Edge Sparsification for TSP

GES-TSP：用于旅行商问题的图边稀疏化方法

Abstract: Solving large-scale instances of the Traveling Salesman Problem (TSP) exactly is computationally expensive. Researchers often employ graph sparsification methods to improve computational efficiency. Traditional sparsification methods typically rely on fixed heuristics and fail to fully exploit instance-specific structural information.

摘要： 精确求解大规模旅行商问题（TSP）的计算成本高昂。研究人员通常采用图稀疏化方法来提高计算效率。传统的稀疏化方法通常依赖于固定的启发式规则，未能充分利用特定实例的结构信息。

In this paper, we propose Graph Edge Sparsification (GES), a learning-based sparsification approach for Euclidean TSP. By incorporating geometric structural information and combinatorial optimization technology, our proposed method adaptively generates a sparsification graph for different instances, significantly reducing the graph size and accelerating the solving process.

在本文中，我们提出了一种用于欧几里得 TSP 的基于学习的稀疏化方法——图边稀疏化（GES）。通过结合几何结构信息和组合优化技术，我们提出的方法能够针对不同实例自适应地生成稀疏图，从而显著减小图规模并加速求解过程。

Experimental results demonstrate that our sparsification method can prune up to 95% of edges on the MATILDA dataset, while keeping the solution gap within 1% of the optimal value. Moreover, our approach exhibits strong generalization capability on the TSPLIB. On some large-scale instances, the pruning rate exceeds 99%, while the optimality gap remains below 1%.

实验结果表明，我们的稀疏化方法在 MATILDA 数据集上可以剪枝高达 95% 的边，同时将解的差距保持在最优值的 1% 以内。此外，我们的方法在 TSPLIB 上表现出强大的泛化能力。在某些大规模实例中，剪枝率超过了 99%，而最优性差距仍保持在 1% 以下。

---

Paper Details:

• Authors: Tianfeng Chen, Xianyue Li
• Date: 23 Jun 2026
• Subjects: Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Combinatorics (math.CO)
• DOI: 10.48550/arXiv.2607.09708

论文详情：

• 作者： Tianfeng Chen, Xianyue Li
• 日期： 2026年6月23日
• 学科： 人工智能 (cs.AI)；机器学习 (cs.LG)；组合数学 (math.CO)
• DOI： 10.48550/arXiv.2607.09708