# Hybrid Pointer Networks for Traveling Salesman Problems Optimization

arXiv: https://arxiv.org/abs/2110.03104 · HTML: https://mlsanity.com/paper/2110.03104/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 6 Oct 2021.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [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)
- [Self-critical Sequence Training for Image Captioning](https://mlsanity.com/paper/1612.00563/) (2016)
- [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)
- [Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learning](https://mlsanity.com/paper/1911.04936/) (2019)
- [The Transformer Network for the Traveling Salesman Problem](https://mlsanity.com/paper/2103.03012/) (2021)
- [Dynamic Partial Removal: A Neural Network Heuristic for Large Neighborhood Search](https://mlsanity.com/paper/2005.09330/) (2020)

## Built on by (most cited first, 4 of 4)

- [A Survey on Service Route and Time Prediction in Instant Delivery: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2309.01194/) (2023)
- [A Lightweight CNN-Transformer Model for Learning Traveling Salesman Problems](https://mlsanity.com/paper/2305.01883/) (2023)
- [All You Need is an Improving Column: Enhancing Column Generation for Parallel Machine Scheduling via Transformers](https://mlsanity.com/paper/2410.15601/) (2024)
- [Onboard Mission Replanning for Adaptive Cooperative Multi-Robot Systems](https://mlsanity.com/paper/2506.06094/) (2025)

## Abstract (arXiv)

In this work, a novel idea is presented for combinatorial optimization problems, a hybrid network, which results in a superior outcome. We applied this method to graph pointer networks [1], expanding its capabilities to a higher level. We proposed a hybrid pointer network (HPN) to solve the travelling salesman problem trained by reinforcement learning. Furthermore, HPN builds upon graph pointer networks which is an extension of pointer networks with an additional graph embedding layer. HPN outperforms the graph pointer network in solution quality due to the hybrid encoder, which provides our model with a verity encoding type, allowing our model to converge to a better policy. Our network significantly outperforms the original graph pointer network for small and large-scale problems increasing its performance for TSP50 from 5.959 to 5.706 without utilizing 2opt, Pointer networks, Attention model, and a wide range of models, producing results comparable to highly tuned and specialized algorithms. We make our data, models, and code publicly available [2].