Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization

Computer Science > Artificial Intelligence [Submitted on 28 Mar 2026] Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization Shaodi Feng, Zhuoyi Lin, Yaoxin Wu, Haiyan Yin, Yan Jin, Senthilnath Jayavelu, Xun Xu Recent research has demonstrated the effectiveness of large language models (LLMs) in solving combinatorial optimization problems (COPs) by representing tasks and instances in natural language. However, purely language-based approaches struggle to accurately capture complex relational structures inherent in many COPs, rendering them less effective at addressing medium-sized or larger instances. To address these limitations, we propose AlignOPT, a novel approach that aligns LLMs with graph neural solvers to learn a more generalizable neural COP heuristic. Specifically, AlignOPT leverages the semantic understanding capabilities of LLMs to encode textual descriptions of COPs and their instances, while concurrently exploiting graph neural solvers to explicitly model the underlying graph structures of COP instances. Our approach facilitates a robust integration and alignment between linguistic semantics and structural representations, enabling more accurate and scalable COP solutions. Experimental results demonstrate that AlignOPT achieves state-of-the-art results across diverse COPs, underscoring its effectiveness in aligning semantic and structural representations. In particular, AlignOPT demonstrates strong generalization, effectively extending to previously unseen COP instances. Comments: 18 pages, 3 figures Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2603.27169 [cs.AI]   (or arXiv:2603.27169v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.27169 Focus to learn more Submission history From: Zhuoyi Lin [view email] [v1] Sat, 28 Mar 2026 07:07:56 UTC (188 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)