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arXiv · 2609.37175

VLM Fine-Tuning for End-to-End Combinatorial Optimization

Qingsong Yan·Xia Jiang·Yaoxin Wu·Wen Song·Lu Zhang·Yingjie Zhou
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Abstract

Large language models (LLMs) have provided a unified interface for end-to-end combinatorial optimization (CO), but textual serialization alone may obscure spatial and relational structures that are important for generating effective CO solutions. This paper presents a general-purpose vision-language solver that augments textual instance descriptions with input-derived visual representations. A single vision-language model (VLM) is applied across different CO tasks and trained using supervised fine-tuning followed by verifier-guided reinforcement learning. While the visual inputs contain no gold solutions or solution-derived information, our experiments show that the VLM generally improves solution quality over its text-only counterpart, with particularly clear gains on more complex CO problems such as CVRP and JSSP. The advantage of visual information is more pronounced at large problem scales.

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Qingsong Yan, Xia Jiang, Yaoxin Wu, Wen Song, Lu Zhang, Yingjie Zhou. 2026-09-29. VLM Fine-Tuning for End-to-End Combinatorial Optimization. https://arxiv.org/abs/2609.37175

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