AGDN: Learning to Solve Traveling Salesman Problem with Anisotropic Graph Diffusion Network

2026-06-17

AI Summary

This work addresses the challenges in solving the Traveling Salesman Problem (TSP) posed by fully connected graphs lacking topological priors and the risk of discarding optimal edges during graph sparsification. To overcome these issues, the authors propose the Anisotropic Graph Diffusion Network (AGDN), which innovatively integrates node similarity and geometric distance to construct a MixScore transition matrix. AGDN employs an anisotropic diffusion mechanism that enables efficient multi-hop information propagation, allowing structural information to be thoroughly disseminated before sparsification. This approach preserves critical edges while enhancing model generalization. Extensive experiments demonstrate that AGDN consistently outperforms existing methods across TSP instances of varying sizes and distributions, achieving high solution quality, computational efficiency, and strong generalization to unseen problem scales and distributions.

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.

Problem

• Traveling Salesman Problem
• Graph Neural Network
• Graph Sparsification
• Topological Prior
• Combinatorial Optimization

Innovation

• Anisotropic Graph Diffusion
• MixScore Transition Matrix
• Graph Neural Network
• Traveling Salesman Problem
• Graph Sparsification