We propose UTSP, an unsupervised learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge to be part of the optimal path. We then apply local search to generate our final prediction based on the heat map. Our loss function consists of two parts: one pushes the model to find the shortest path and the other serves as a surrogate for the constraint that the route should form a Hamiltonian Cycle. Experimental results show that UTSP outperforms the existing data-driven TSP heuristics. Our approach is parameter efficient as well as data efficient: the model takes $\sim$ 10\% of the number of parameters and $\sim$ 0.2\% of training samples compared with reinforcement learning or supervised learning methods.

翻译：我们提出UTSP，一种用于求解旅行商问题（TSP）的无监督学习（UL）框架。我们使用代理损失函数训练图神经网络（GNN）。该GNN输出一个热力图，表示每条边属于最优路径的概率。然后，我们基于热力图应用局部搜索生成最终预测结果。损失函数由两部分组成：一部分推动模型寻找最短路径，另一部分作为约束条件代理，确保路径形成哈密顿回路。实验结果表明，UTSP优于现有数据驱动的TSP启发式方法。我们的方法兼具参数高效性和数据高效性：与强化学习或监督学习方法相比，模型参数数量仅需约10%，训练样本仅需约0.2%。