[2603.27169] Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization

Computer Science > Artificial Intelligence arXiv:2603.27169 (cs) [Submitted on 28 Mar 2026] Title:Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization Authors:Shaodi Feng, Zhuoyi Lin, Yaoxin Wu, Haiyan Yin, Yan Jin, Senthilnath Jayavelu, Xun Xu View a PDF of the paper titled Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization, by Shaodi Feng and 5 other authors View PDF HTML (experimental) Abstract: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-o...