# ViTSP: A Vision Language Models Guided Framework for Solving Large-Scale Traveling Salesman Problems

arXiv: https://arxiv.org/abs/2509.23465 · HTML: https://mlsanity.com/paper/2509.23465/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in VLM benchmarks and visual reasoning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Placed in

- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [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)
- [LLM Post-Training: A Deep Dive into Reasoning Large Language Models](https://mlsanity.com/paper/2502.21321/) (2025)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [Learning to Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2110.07983/) (2021)
- [Learning the Travelling Salesperson Problem Requires Rethinking Generalization](https://mlsanity.com/paper/2006.07054/) (2020)
- [GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time](https://mlsanity.com/paper/2312.08224/) (2023)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmark](https://mlsanity.com/paper/2306.17100/) (2023)
- [Graph Neural Network Guided Local Search for the Traveling Salesperson Problem](https://mlsanity.com/paper/2110.05291/) (2021)
- [Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem](https://mlsanity.com/paper/2304.09407/) (2023)
- [UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems](https://mlsanity.com/paper/2407.00312/) (2024)
- [Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimization](https://mlsanity.com/paper/2502.02941/) (2025)
- [INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer](https://mlsanity.com/paper/2402.02317/) (2024)
- [H-TSP: Hierarchically Solving the Large-Scale Travelling Salesman Problem](https://mlsanity.com/paper/2304.09395/) (2023)
- [A Survey of In-Context Reinforcement Learning](https://mlsanity.com/paper/2502.07978/) (2025)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [Visual Reasoning and Multi-Agent Approach in Multimodal Large Language Models (MLLMs): Solving TSP and mTSP Combinatorial Challenges](https://mlsanity.com/paper/2407.00092/) (2024)
- [Reinforced Lin-Kernighan-Helsgaun Algorithms for the Traveling Salesman Problems](https://mlsanity.com/paper/2207.03876/) (2022)
- [Learning-Based TSP-Solvers Tend to Be Overly Greedy](https://mlsanity.com/paper/2502.00767/) (2025)

## Built on by (most cited first, 1 of 1)

- [Graph Neural Network-based Algorithm Selection for the Traveling Salesman Problem: A Systematic Study of Cost and Rank Losses under Distinct Budget Regimes](https://mlsanity.com/paper/2607.18632/) (2026)

## Abstract (arXiv)

Solving the Traveling Salesman Problem (TSP) is NP-hard yet fundamental for a wide range of real-world applications. Classical exact methods face challenges in scaling, and heuristic methods often require domain-specific parameter calibration. While learning-based approaches have shown promise, they suffer from poor generalization and limited scalability due to fixed training data. This work proposes ViTSP, a novel framework that leverages pre-trained vision language models (VLMs) to visually guide the solution process for large-scale TSPs. The VLMs function to identify promising small-scale subproblems from a visualized TSP instance, which are then efficiently optimized using an off-the-shelf solver to improve the global solution. ViTSP bypasses the dedicated model training at the user end while maintaining effectiveness across diverse instances. Experiments on real-world TSP instances ranging from 1k to 88k nodes demonstrate that ViTSP consistently achieves solutions with average optimality gaps of 0.24%, outperforming existing learning-based methods. Under the same runtime budget, it surpasses the best-performing heuristic solver, LKH-3, by reducing its gaps by 3.57% to 100%, particularly on very-large-scale instances with more than 10k nodes. Our framework offers a new perspective in hybridizing pre-trained generative models and operations research solvers in solving combinatorial optimization problems. The framework holds potential for integration into more complex real-world logistics systems. The code is available at https://github.itap.purdue.edu/uSMART/ViTSP_ICLR2026.