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

Zhuoli Yin, Yi Ding, Reem Khir, Hua Cai

TL;DR

ViTSP is proposed, a novel framework that leverages pre-trained vision language models (VLMs) to visually guide the solution process for large-scale TSPs, outperforming existing learning-based methods and offering a new perspective in hybridizing pre-trained generative models and operations research solvers in solving combinatorial optimization problems.

Abstract

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.

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

TL;DR

ViTSP is proposed, a novel framework that leverages pre-trained vision language models (VLMs) to visually guide the solution process for large-scale TSPs, outperforming existing learning-based methods and offering a new perspective in hybridizing pre-trained generative models and operations research solvers in solving combinatorial optimization problems.

Abstract

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.

Paper Structure

This paper contains 37 sections, 2 equations, 7 figures, 7 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related works
  3. OR approaches
  4. Learning-based approaches
  5. LLMs/VLMs-based approaches
  6. Methods
  7. Preliminary: Traveling Salesman Problem (TSP)
  8. Solution initialization
  9. Visual selection of subproblems by VLMs
  10. Subproblem optimization
  11. Reformulating subproblems
  12. Solving and recovering the solution for the original TSP
  13. Asynchronous orchestration
  14. Experiments and results analysis
  15. Experimental setups
  16. ...and 22 more sections

Figures (7)

  • Figure 1: The vision-guided framework (ViTSP) for large-scale TSP, where pre-trained VLMs and off-the-shelf solvers are asynchronously coordinated to identify and optimize subproblems, respectively.
  • Figure 2: Optimality gaps over time on selected instances between ViTSP and LKH-3 (more RUNS).
  • Figure 3: Ablation studies of different selection policies on selected instances.
  • Figure 4: An example of the visual prompt to VLMs. In this example, nrw1379 is used. The tour is initialized by LKH-3.
  • Figure 5: Optimality gap reduction over time between ViTSP and LKH-3 (more RUNS).
  • ...and 2 more figures