Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization
Summary: arXiv:2603.27169v1 Announce Type: new
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.
Introduction
Combinatorial optimization problems are a fundamental aspect of computer science and operations research, posing significant challenges due to their complexity and the intricacies involved in finding optimal solutions. Recent advances in artificial intelligence, particularly large language models (LLMs), have shown promise in representing and solving these problems. Nevertheless, there are notable limitations when LLMs are applied solely through a language-centric approach.
Challenges in Current Approaches
While LLMs excel at understanding and generating human-like text, they face difficulties in:
- Accurately representing complex relational structures.
- Scaling to medium-sized or larger instances of combinatorial problems.
- Integrating relational understanding with problem-solving capabilities.
Introducing AlignOPT
AlignOPT is designed to overcome the limitations associated with traditional LLM approaches by:
- Leveraging the semantic understanding capabilities of LLMs to encode textual descriptions of COPs and their instances.
- Utilizing graph neural solvers to explicitly model the underlying graph structures of COP instances.
This dual approach allows AlignOPT to create a more generalizable neural heuristic that can adapt to various combinatorial optimization scenarios.
Integration of Linguistic Semantics and Structural Representations
The integration of linguistic and structural representations in AlignOPT facilitates a more robust understanding and solution mechanism for COPs. By aligning the two domains, the model can more accurately reflect the intricate relationships found within complex optimization tasks.
Experimental Results
Experimental results indicate that AlignOPT outperforms existing methods, achieving state-of-the-art results across diverse types of COPs. Key findings include:
- Enhanced accuracy in problem-solving compared to previous LLM-based approaches.
- Strong generalization capabilities, enabling the model to effectively handle previously unseen COP instances.
- Significant improvements in scalability, making it feasible to tackle larger problem sets.
Conclusion
The introduction of AlignOPT marks a significant advancement in the intersection of language models and graph theory for combinatorial optimization. By addressing the limitations of previous approaches, AlignOPT not only enhances the efficacy of solving COPs but also paves the way for future research in aligning linguistic semantics with structural representations. The promising results and generalization capabilities highlight AlignOPT’s potential to redefine solutions in combinatorial optimization.