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.

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