Algorithm design 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. In just a few years, this integration has yielded remarkable progress in areas ranging from combinatorial optimization to scientific discovery. Despite this rapid expansion, a holistic understanding of the field is hindered by the lack of a systematic review, as existing surveys either remain limited to narrow sub-fields or with different objectives. This paper seeks to provide a systematic review of algorithm design with LLMs. We introduce a taxonomy that categorises the roles of LLMs as optimizers, predictors, extractors and designers, analyzing the progress, advantages, and limitations within each category. We further synthesize literature across the three phases of the algorithm design pipeline and across diverse algorithmic applications that define the current landscape. Finally, we outline key open challenges and opportunities to guide future research.

翻译：算法设计是各领域有效解决问题的关键。大语言模型（LLMs）的出现显著提升了该领域的自动化和创新能力，提供了新的视角和有前景的解决方案。短短几年内，这种融合已在从组合优化到科学发现的广泛领域取得了显著进展。尽管发展迅速，但由于缺乏系统性综述，对该领域的整体理解仍存在障碍——现有综述要么局限于狭窄的子领域，要么目标不同。本文旨在对基于LLMs的算法设计进行系统性综述。我们提出了一种分类法，将LLMs的角色划分为优化器、预测器、提取器和设计器，并分析了各类别的进展、优势与局限。我们进一步综合了算法设计流程三个阶段以及定义当前格局的多样化算法应用的相关文献。最后，我们概述了关键的开放挑战与机遇，以指导未来研究。