Title: ViTSP: A Vision Language Models Guided Framework for Large-Scale Traveling Salesman Problems
Primary area: optimization
Keywords: Machine Learning, Large Language Model, Traveling Salesman Problem, Combinatorial Optimization

Abstract: Solving Traveling Salesman Problem (TSP) is NP-hard yet fundamental for wide 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 below 0.2\%, outperforming existing learning-based methods. Under the same runtime budget, it surpasses the best-performing heuristic solver, LKH-3, by reducing its gaps by 12\% 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, with practical implications for integration into more complex logistics systems.  The code is available at https://anonymous.4open.science/r/ViTSP_codes-6683.