Large Language Models (LLMs) possess substantial reasoning capabilities and are increasingly applied to optimization tasks, particularly in synergy with evolutionary computation. However, while recent surveys have explored specific aspects of this domain, they lack an integrative perspective that connects problem modeling with solving workflows. To address this gap, we present a systematic review of recent developments and organize them within a structured framework. First, we classify existing research into two primary stages: LLMs for optimization modeling and LLMs for optimization solving. Second, we divide the latter into three paradigms based on the role of the LLM: stand-alone optimizers, low-level components embedded within algorithms, and high-level managers for algorithm selection and generation. Third, for each category, we analyze representative methods, distill technical challenges, and examine their interplay with traditional approaches. Finally, we review interdisciplinary applications across the natural sciences, engineering, and machine learning. Based on this analysis, we highlight key limitations and point toward future directions for developing self-evolving agentic ecosystems. An up-to-date collection of related literature is maintained at https://github.com/ishmael233/LLM4OPT.

翻译：大语言模型（LLMs）具备强大的推理能力，正日益广泛地应用于优化任务，特别是与进化计算协同工作。然而，尽管近期的综述性研究探讨了该领域的特定方面，但它们缺乏将问题建模与求解流程相连接的整合性视角。为弥补这一空白，我们对最新进展进行了系统性回顾，并将其组织在一个结构化框架内。首先，我们将现有研究划分为两个主要阶段：用于优化建模的LLMs和用于优化求解的LLMs。其次，我们根据LLM所扮演的角色，将后者进一步划分为三种范式：独立优化器、嵌入算法内部的底层组件，以及用于算法选择与生成的高层管理器。第三，针对每个类别，我们分析了代表性方法，提炼了技术挑战，并审视了它们与传统方法的相互作用。最后，我们回顾了跨自然科学、工程学及机器学习领域的交叉应用。基于此分析，我们指出了关键局限性，并指明了未来开发自进化智能体生态系统的发展方向。相关文献的最新集合维护于 https://github.com/ishmael233/LLM4OPT。