Algorithm Design (AD) is crucial for effective problem-solving across various domains. The advent of Large Language Models (LLMs) has notably enhanced the automation and innovation within this field, offering new perspectives and promising solutions. Over the past three years, the integration of LLMs into AD (LLM4AD) has seen substantial progress, with applications spanning optimization, machine learning, mathematical reasoning, and scientific discovery. Given the rapid advancements and expanding scope of this field, a systematic review is both timely and necessary. This paper provides a systematic review of LLM4AD. First, we offer an overview and summary of existing studies. Then, we introduce a taxonomy and review the literature across four dimensions: the roles of LLMs, search methods, prompt methods, and application domains with a discussion of potential and achievements of LLMs in AD. Finally, we identify current challenges and highlight several promising directions for future research.

翻译：算法设计（AD）对于跨领域的高效问题求解至关重要。大语言模型（LLM）的出现显著推动了该领域自动化和创新能力的提升，提供了新的视角和极具前景的解决方案。过去三年间，大语言模型与算法设计的融合（LLM4AD）取得了实质性进展，其应用遍及优化、机器学习、数学推理与科学发现等多个方向。鉴于该领域的快速发展和不断扩大的研究范围，进行一次系统性综述既及时又必要。本文对LLM4AD领域进行了系统性综述。首先，我们对现有研究进行了概述与总结。随后，我们提出了一个分类体系，并从四个维度对相关文献进行了梳理：大语言模型在算法设计中的角色、搜索方法、提示方法以及应用领域，并探讨了大语言模型在算法设计中的潜力与已取得的成果。最后，我们指出了当前面临的挑战，并展望了未来研究中若干富有前景的方向。