The omnipresence of NP-hard combinatorial optimization problems (COPs) compels domain experts to engage in trial-and-error heuristic design. The long-standing endeavor of design automation has gained new momentum with the rise of large language models (LLMs). This paper introduces Language Hyper-Heuristics (LHHs), an emerging variant of Hyper-Heuristics that leverages LLMs for heuristic generation, featuring minimal manual intervention and open-ended heuristic spaces. To empower LHHs, we present Reflective Evolution (ReEvo), a novel integration of evolutionary search for efficiently exploring the heuristic space, and LLM reflections to provide verbal gradients within the space. Across five heterogeneous algorithmic types, six different COPs, and both white-box and black-box views of COPs, ReEvo yields state-of-the-art and competitive meta-heuristics, evolutionary algorithms, heuristics, and neural solvers, while being more sample-efficient than prior LHHs.

翻译：NP难组合优化问题（COP）的普遍性迫使领域专家进行试错式的启发式设计。随着大型语言模型（LLM）的兴起，设计自动化的长期努力获得了新的动力。本文介绍了语言超启发式算法（LHH），这是一种新兴的超启发式算法变体，它利用LLM进行启发式生成，具有最小化人工干预和开放式启发式空间的特点。为了增强LHH的能力，我们提出了反思进化（ReEvo），这是一种新颖的集成方法，它结合了进化搜索以高效探索启发式空间，以及LLM反思以在空间内提供语言梯度。在五种异构算法类型、六个不同的COP问题，以及COP的白盒与黑盒视角下，ReEvo均能生成最先进且具有竞争力的元启发式算法、进化算法、启发式算法和神经求解器，同时比先前的LHH具有更高的样本效率。