# CycleFormer : TSP Solver Based on Language Modeling

arXiv: https://arxiv.org/abs/2405.20042 · HTML: https://mlsanity.com/paper/2405.20042/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
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- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [DeepSpeed Inference: Enabling Efficient Inference of Transformer Models at Unprecedented Scale](https://mlsanity.com/paper/2207.00032/) (2022)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformer](https://mlsanity.com/paper/2110.02544/) (2021)
- [The Transformer Network for the Traveling Salesman Problem](https://mlsanity.com/paper/2103.03012/) (2021)
- [Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem](https://mlsanity.com/paper/2304.09407/) (2023)
- [BARD: A structured technique for group elicitation of Bayesian networks to support analytic reasoning](https://mlsanity.com/paper/2003.01207/) (2020)
- [Retention Is All You Need](https://mlsanity.com/paper/2304.03103/) (2023)

## Abstract (arXiv)

We propose a new transformer model for the Traveling Salesman Problem (TSP) called CycleFormer. We identified distinctive characteristics that need to be considered when applying a conventional transformer model to TSP and aimed to fully incorporate these elements into the TSP-specific transformer. Unlike the token sets in typical language models, which are limited and static, the token (node) set in TSP is unlimited and dynamic. To exploit this fact to the fullest, we equated the encoder output with the decoder linear layer and directly connected the context vector of the encoder to the decoder encoding. Additionally, we added a positional encoding to the encoder tokens that reflects the two-dimensional nature of TSP, and devised a circular positional encoding for the decoder tokens that considers the cyclic properties of a tour. By incorporating these ideas, CycleFormer outperforms state-of-the-art (SOTA) transformer models for TSP from TSP-50 to TSP-500. Notably, on TSP-500, the optimality gap was reduced by approximately 2.8 times, from 3.09% to 1.10%, compared to the existing SOTA. The code will be made available at https://github.com/Giventicket/CycleFormer.