# Reinforcement Learning-based Non-Autoregressive Solver for Traveling Salesman Problems

arXiv: https://arxiv.org/abs/2308.00560 · HTML: https://mlsanity.com/paper/2308.00560/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 55 references that are in the map.
- First posted on arXiv 1 Aug 2023.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Six Challenges for Neural Machine Translation](https://mlsanity.com/paper/1706.03872/) (2017)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Neural Machine Translation: A Review and Survey](https://mlsanity.com/paper/1912.02047/) (2019)
- [Learning the Travelling Salesperson Problem Requires Rethinking Generalization](https://mlsanity.com/paper/2006.07054/) (2020)
- [Deep Policy Dynamic Programming for Vehicle Routing Problems](https://mlsanity.com/paper/2102.11756/) (2021)
- [Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1911.04936/) (2019)
- [Graph Neural Network Guided Local Search for the Traveling Salesperson Problem](https://mlsanity.com/paper/2110.05291/) (2021)
- [The Transformer Network for the Traveling Salesman Problem](https://mlsanity.com/paper/2103.03012/) (2021)
- [Guiding Non-Autoregressive Neural Machine Translation Decoding with Reordering Information](https://mlsanity.com/paper/1911.02215/) (2019)
- [Meta-Learning-Based Deep Reinforcement Learning for Multiobjective Optimization Problems](https://mlsanity.com/paper/2105.02741/) (2021)
- [Divide and Conquer Networks](https://mlsanity.com/paper/1611.02401/) (2016)
- [A Lightweight CNN-Transformer Model for Learning Traveling Salesman Problems](https://mlsanity.com/paper/2305.01883/) (2023)

## Built on by (most cited first, 5 of 5)

- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scales](https://mlsanity.com/paper/2506.06634/) (2025)
- [Mechanistic Interpretability for Neural TSP Solvers](https://mlsanity.com/paper/2510.21693/) (2025)
- [Test-Time Augmentation for Traveling Salesperson Problem](https://mlsanity.com/paper/2405.04767/) (2024)

## Abstract (arXiv)

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem with broad real-world applications. Recently, neural networks have gained popularity in this research area because as shown in the literature, they provide strong heuristic solutions to TSPs. Compared to autoregressive neural approaches, non-autoregressive (NAR) networks exploit the inference parallelism to elevate inference speed but suffer from comparatively low solution quality. In this paper, we propose a novel NAR model named NAR4TSP, which incorporates a specially designed architecture and an enhanced reinforcement learning strategy. To the best of our knowledge, NAR4TSP is the first TSP solver that successfully combines RL and NAR networks. The key lies in the incorporation of NAR network output decoding into the training process. NAR4TSP efficiently represents TSP encoded information as rewards and seamlessly integrates it into reinforcement learning strategies, while maintaining consistent TSP sequence constraints during both training and testing phases. Experimental results on both synthetic and real-world TSPs demonstrate that NAR4TSP outperforms five state-of-the-art models in terms of solution quality, inference speed, and generalization to unseen scenarios.