The Traveling Salesman Problem (TSP) is a well-known problem in combinatorial optimization with applications in various domains. However, existing TSP solvers face challenges in producing high-quality solutions with low latency. To address this issue, we propose NAR4TSP, which produces TSP solutions in a Non-Autoregressive (NAR) manner using a specially designed Graph Neural Network (GNN), achieving faster inference speed. Moreover, NAR4TSP is trained using an enhanced Reinforcement Learning (RL) strategy, eliminating the dependency on costly labels used to train conventional supervised learning-based NAR models. To the best of our knowledge, NAR4TSP is the first TSP solver that successfully combines RL and NAR decoding. The experimental results on both synthetic and real-world TSP instances demonstrate that NAR4TSP outperforms four state-of-the-art models in terms of solution quality, inference latency, and generalization ability. Lastly, we present visualizations of NAR4TSP's decoding process and its overall path planning to showcase the feasibility of implementing NAR4TSP in an end-to-end manner and its effectiveness, respectively.

翻译：旅行商问题（TSP）是组合优化中的经典问题，在多个领域具有广泛应用。然而，现有TSP求解器在低延迟下生成高质量解决方案方面仍面临挑战。为解决此问题，我们提出NAR4TSP，该模型采用专门设计的图神经网络（GNN），以非自回归（NAR）方式生成TSP解，显著提升推理速度。此外，NAR4TSP通过增强型强化学习（RL）策略进行训练，消除了传统监督学习型NAR模型对昂贵标签的依赖。据我们所知，NAR4TSP是首个成功结合RL与NAR解码的TSP求解器。在合成及真实TSP实例上的实验结果表明，NAR4TSP在解质量、推理延迟和泛化能力方面均优于四种最先进模型。最后，我们通过可视化NAR4TSP的解码过程及其整体路径规划，分别展示了该模型以端到端方式实现的可行性及其有效性。