We study the generalization capability of Unsupervised Learning in solving the Travelling Salesman Problem (TSP). We use a Graph Neural Network (GNN) trained with a surrogate loss function to generate an embedding for each node. We use these embeddings to construct a heat map that indicates the likelihood of each edge being part of the optimal route. We then apply local search to generate our final predictions. Our investigation explores how different training instance sizes, embedding dimensions, and distributions influence the outcomes of Unsupervised Learning methods. Our results show that training with larger instance sizes and increasing embedding dimensions can build a more effective representation, enhancing the model's ability to solve TSP. Furthermore, in evaluating generalization across different distributions, we first determine the hardness of various distributions and explore how different hardnesses affect the final results. Our findings suggest that models trained on harder instances exhibit better generalization capabilities, highlighting the importance of selecting appropriate training instances in solving TSP using Unsupervised Learning.

翻译：本研究探讨了无监督学习在解决旅行商问题中的泛化能力。我们采用通过代理损失函数训练的图神经网络为每个节点生成嵌入表示，并利用这些嵌入构建热力图以指示各边属于最优路径的可能性，最后通过局部搜索生成最终预测。本研究系统探索了不同训练实例规模、嵌入维度及数据分布如何影响无监督学习方法的效果。实验结果表明：采用更大规模的训练实例并增加嵌入维度能够构建更有效的表征，从而提升模型求解TSP的能力。在评估跨分布泛化性能时，我们首先量化了不同分布的求解难度，进而探究难度差异对最终结果的影响。研究发现，在难度较高的实例上训练的模型展现出更优的泛化性能，这凸显了在基于无监督学习求解TSP时选择适当训练实例的重要性。