标题： 大型语言模型能否作为网络结构组合问题的进化优化器被信任？ 显示英文标题

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

摘要： 大型语言模型（LLMs）在跨多个领域的语言理解和推理方面表现出色。 最近，人们越来越关注利用LLMs不仅作为优化任务的助手，而是作为积极的优化器，特别是针对网络结构的组合问题。 然而，在LLMs可以可靠地部署在此角色之前，必须解决一个基本问题：LLMs能否迭代地操作始终符合问题约束的解决方案？ 在本工作中，我们提出了一种系统框架，以评估LLMs参与问题结构的能力。 我们不将模型视为黑盒生成器，而是采用常用的进化算子作为优化器，并提出了一个全面的评估框架，严格评估LLM生成的算子在进化过程不同阶段的输出保真度。 为了提高鲁棒性，我们引入了一种混合错误纠正机制，以减轻LLM输出中的不确定性。 此外，我们开发了一种成本高效的种群级优化策略，与传统的个体级方法相比，显著提高了效率。 在代表性节点级组合网络优化任务上的大量实验表明了基于LLM的算子的有效性、适应性和固有局限性。 我们的研究结果为将LLMs整合到进化计算中提供了新的视角，为网络化系统中的可扩展优化提供了实用见解。 显示英文摘要

摘要： Large Language Models (LLMs) have shown impressive capabilities in language understanding and reasoning across diverse domains. Recently, there has been increasing interests in utilizing LLMs not merely as assistants in optimization tasks, but as active 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 capacity of LLMs to engage with problem structures. Rather than treating the model as a black-box generator, we adopt the commonly used evolutionary operators as optimizer and propose a comprehensive evaluation framework that rigorously assesses the output fidelity of LLM-generated operators across different stages of the evolutionary process. To enhance robustness, we introduce a hybrid error-correction mechanism that mitigates uncertainty in LLM outputs. Moreover, we develop 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 operators. Our findings offer new perspectives on the integration of LLMs into evolutionary computation, providing practical insights for scalable optimization in networked systems.