Can Large Language Models Be Trusted as Evolutionary Optimizers for Network-Structured Combinatorial Problems?

TL;DR

This paper evaluates the potential of Large Language Models to serve as reliable evolutionary optimizers for network-structured combinatorial problems, introducing a framework for assessing their solution manipulation capabilities.

Contribution

It proposes a systematic evaluation framework and hybrid error-correction mechanism to assess and enhance LLMs' effectiveness as evolutionary operators in combinatorial optimization.

Findings

LLMs can be integrated into evolutionary optimization with certain limitations.

Hybrid error correction improves LLM output fidelity.

Population-level strategies increase optimization efficiency.

Abstract

Large Language Models (LLMs) have shown strong capabilities in language understanding and reasoning across diverse domains. Recently, there has been increasing interest in utilizing LLMs not merely as assistants in optimization tasks, but as primary optimizers, particularly for network-structured combinatorial problems. However, before LLMs can be reliably deployed in this role, a fundamental question must be addressed: Can LLMs iteratively manipulate solutions that consistently adhere to problem constraints? In this work, we propose a systematic framework to evaluate the capability of LLMs to engage with problem structures. Rather than treating the model as a black-box generator, we adopt the commonly used evolutionary optimizer (EVO) and propose a comprehensive evaluation framework that rigorously assesses the output fidelity of LLM-based operators across different stages of the evolutionary process. To enhance robustness, we introduce a hybrid error-correction mechanism that mitigates uncertainty in LLMs outputs. Moreover, we explore a cost-efficient population-level optimization strategy that significantly improves efficiency compared to traditional individual-level approaches. Extensive experiments on a representative node-level combinatorial network optimization task demonstrate the effectiveness, adaptability, and inherent limitations of LLM-based EVO. Our findings present perspectives on integrating LLMs into evolutionary computation and discuss paths that may support scalable and context-aware optimization in networked systems.