A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving

Large Language Models (LLMs), with their strong understanding and reasoning capabilities, are increasingly being explored for tackling optimization problems, especially in synergy with evolutionary computation. Despite rapid progress, however, the field still lacks a unified synthesis and a systematic taxonomy. This survey addresses this gap by providing a comprehensive review of recent developments and organizing them within a structured framework. We classify existing research into two main stages: LLMs for optimization modeling and LLMs for optimization solving. The latter is further divided into three paradigms according to the role of LLMs in the optimization workflow: LLMs as stand-alone optimizers, low-level LLMs embedded within optimization algorithms, and high-level LLMs for algorithm selection and generation. For each category, we analyze representative methods, distill technical challenges, and examine their interplay with traditional approaches. We also review interdisciplinary applications spanning the natural sciences, engineering, and machine learning. By contrasting LLM-driven and conventional methods, we highlight key limitations and research gaps, and point toward future directions for developing self-evolving agentic ecosystems for optimization. An up-to-date collection of related literature is maintained at https://github.com/ishmael233/LLM4OPT.