AGDN: Learning to Solve Traveling Salesman Problem with Anisotropic Graph Diffusion Network
For researchers in combinatorial optimization and graph neural networks, AGDN provides a more effective way to exploit graph structure in TSP, addressing key limitations of prior approaches.
The paper introduces the Anisotropic Graph Diffusion Network (AGDN) for solving the Traveling Salesman Problem, achieving consistent performance improvements over existing methods across various instance sizes and distributions while maintaining competitive computation time.
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.