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

TL;DR

This work investigates whether large language models can serve as reliable evolutionary optimizers for network-structured combinatorial problems. It introduces a structured EVO framework with LLM-based initialization, selection, crossover, and mutation, coupled with a rigorous repair mechanism and a population-level optimization variant to improve efficiency and coherence. Through extensive node-level experiments across multiple networks and language models, the study demonstrates that LLMs can perform EVO operators with competitive performance, while highlighting critical limitations in reliability, token-cost, and scalability, especially for larger graphs and less capable models. The findings offer practical guidance for integrating LLMs into evolutionary computation and point to promising directions such as multimodal inputs and tool-assisted reasoning to realize scalable, context-aware optimization in networked systems.

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.

Figures (10)

• Figure 1: (A) The diagram of LLM-based EVO with the proposed validation and repair mechanism. All four phases of evolutionary optimization, along with the repair process, are based on LLMs. (B) The illustration of population- and individual-level LLM-based EVO. (C) An example of errors encountered in population-level LLM-based crossover. The error message (if any), customized corrected prompt, and previous deficient output will be provided to LLMs for repair.
• Figure 2: Average fitness over generations using LLM-based initialization versus random initialization on the Netscience and Erods datasets. The backbone LLM is GPT-4.0.
• Figure 3: Average fitness over generations for LLM-based, no selection, random selection, roulette, and tournament strategies on Netscience, Erods, and Email datasets. The backbone LLM is GPT-4.0.
• Figure 4: Average fitness over generations for population-level (LLM-P) and individual-level (LLM-S) LLM-based optimizers using GPT-4.0 and GPT-3.5, compared to code-based optimization on Netscience, Erods, and Email datasets.
• Figure 5: Distribution of moderate error outcomes across evolutionary phases for GPT-3.5 and GPT-4.0 generated outputs.