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 progressed significantly, finding applications in diverse areas such as optimization, machine learning, mathematical reasoning, and scientific discovery. Given the rapid development and broadening scope of this field, a systematic review is both timely and essential. This paper provides a systematic review of the works on LLM4AD. First, we present an overview and summary of existing studies. Then, we present a systematic taxonomy and a review of existing works along four dimensions, including the role of LLMs, search techniques, prompt strategies, and applications, with a discussion of the potential and achievements of using LLMs. Finally, we explore current challenges and propose several open questions and promising directions for future research.

翻译：算法设计（AD）对于跨领域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的自动化与创新进程，为算法设计提供了新视角和具有前景的解决方案。过去三年来，大语言模型与算法设计的融合（LLM4AD）取得了显著进展，在优化、机器学习、数学推理和科学发现等多个领域得到应用。鉴于该领域的快速发展和不断扩大的研究范围，进行系统性综述既及时又必要。本文对LLM4AD相关研究进行了系统性综述。首先，我们对现有研究进行了概述与总结。随后，我们从四个维度提出了系统分类框架并对现有工作进行了评述，包括大语言模型的作用、搜索技术、提示策略及应用领域，同时探讨了使用大语言模型的潜力与已取得的成果。最后，我们分析了当前面临的挑战，并提出了若干开放性问题及未来研究的潜在方向。