Publication Type

Conference Proceeding Article

Version

publishedVersion

Publication Date

8-2026

Abstract

The Traveling Salesman Problem (TSP) is a cornerstone of combinatorial optimization and arises in many practical scenarios. Although graph-based learning approaches have been explored for TSP, the question of how to exploit graph structure more effectively remains open. We present the Anisotropic Graph Diffusion Network (AGDN), a new Graph Neural Network framework designed to solve TSP. Our method tackles two central difficulties: (1) the lack of informative topological prior in fully connected TSP graphs, and (2) losing connected nodes in the optimal solution after the commonly used graph sparsification techniques. To overcome these issues, we construct a MixScore transition matrix that merges node similarity with pairwise distance, and we develop an anisotropic graph diffusion strategy that supports efficient information exchange across multiple hops. Comprehensive experiments spanning diverse instance sizes and node distributions show that AGDN consistently outperforms existing methods while keeping computation time competitive. Furthermore, AGDN generalizes well to problem sizes and distributions beyond those seen during training. The implementation is publicly available at: https://github.com/LabRAI/AGDN.

Keywords

Traveling Salesman Problem, Graph Neural Networks

Discipline

Artificial Intelligence and Robotics | Operations Research, Systems Engineering and Industrial Engineering

Research Areas

Intelligent Systems and Optimization

Areas of Excellence

Sustainability

Publication

KDD '26: Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2, Jeju Island, South Korea, August 9-13

First Page

4173

Last Page

4184

Identifier

10.1145/3770855.3817789

Publisher

ACM

City or Country

New York

Additional URL

https://doi.org/10.1145/3770855.3817789

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