GraphThought: Graph Combinatorial Optimization with Thought Generation

Large language models (LLMs) have demonstrated remarkable capabilities across various domains, especially in text processing and generative tasks. Recent advancements in the reasoning capabilities of state-of-the-art LLMs, such as OpenAI-o1, have significantly broadened their applicability, particularly in complex problem-solving and logical inference. However, most existing LLMs struggle with notable limitations in handling graph combinatorial optimization (GCO) problems. To bridge this gap, we formally define the Optimal Thoughts Design (OTD) problem, including its state and action thought space. We then introduce a novel framework, GraphThought, designed to generate high-quality thought datasets for GCO problems. Leveraging these datasets, we fine-tune the Llama-3-8B-Instruct model to develop Llama-GT. Notably, despite its compact 8B-parameter architecture, Llama-GT matches the performance of state-of-the-art LLMs on the GraphArena benchmark. Experimental results show that our approach outperforms both proprietary and open-source models, even rivaling specialized models like o1-mini. This work sets a new state-of-the-art benchmark while challenging the prevailing notion that model scale is the primary driver of reasoning capability.