Metaheuristics and Large Language Models Join Forces: Toward an Integrated Optimization Approach

TL;DR

This study introduces a novel integration of large language models as pattern-recognition engines to guide a BRKGA-based metaheuristic for a social-network optimization task (k-dominating set / multi-hop influence maximization). By designing structured prompts and deriving LLM-based node-importance probabilities pLLM(v), the BRKGA decoder is biased via a modified scoring function, achieving superior solution quality compared to pure BRKGA and a DL-guided variant. The empirical evaluation across synthetic and real-world graphs demonstrates significant gains in performance, with an emphasis on prompt quality and the trade-off between LLM-guided guidance and model-based tuning. The OptiPattern tool is released to enable reproducibility, highlighting the potential and challenges of using LLMs for pattern recognition in combinatorial optimization and paving the way for larger-scale, affordable integrations.

Abstract

Since the rise of Large Language Models (LLMs) a couple of years ago, researchers in metaheuristics (MHs) have wondered how to use their power in a beneficial way within their algorithms. This paper introduces a novel approach that leverages LLMs as pattern recognition tools to improve MHs. The resulting hybrid method, tested in the context of a social network-based combinatorial optimization problem, outperforms existing state-of-the-art approaches that combine machine learning with MHs regarding the obtained solution quality. By carefully designing prompts, we demonstrate that the output obtained from LLMs can be used as problem knowledge, leading to improved results. Lastly, we acknowledge LLMs' potential drawbacks and limitations and consider it essential to examine them to advance this type of research further. Our method can be reproduced using a tool available at: https://github.com/camilochs/optipattern.