ES-AHD：一种用于自动启发式设计的进化策略框架
ES-AHD: An Evolution Strategy Framework for Automatic Heuristic Design
- Guangdong University of Technology（广东工业大学）
- School of Mathematics and Statistics（数学与统计学院）
- Xidian University（西安电子科技大学）
- School of Computer Science and Technology（计算机科学与技术学院）
- Beijing Normal University（北京师范大学）
- School of Systems Science（系统科学学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出将进化策略与LLM驱动的自动启发式设计融合的ES-AHD框架，通过语义重组与随机协方差适配机制解决现有进化方法的问题，实现高效的启发式算法生成。
AI中文摘要：
本文提出了ES-AHD，这是一种将进化策略（Evolution Strategy，ES）与大语言模型（Large Language Model，LLM）驱动的自动启发式设计（Automatic Heuristic Design，AHD）深度融合的新型框架。现有进化方法主要依赖随机的个体层面变异，导致搜索盲目、探索与利用失衡。为解决这些问题，ES-AHD引入两项核心机制：其一，基于LLM的语义重组摒弃传统点对点复制，利用LLM的上下文推理能力从表现最优的个体中显式提取核心见解，建立有前景的语义搜索方向，将随机代码变异转化为受ES启发的、以中心为导向的针对性采样；其二，基于温度采样的随机协方差适配动态应对探索-利用困境，通过将ES中的协方差矩阵映射到LLM的采样温度，采用带动量的随机随机游走机制，该机制主要缩小微观代码优化的搜索范围，同时保留偶尔采样更高温度以逃离语义局部最优的关键能力。最终，ES-AHD提供了一种高度定向、鲁棒且高效的搜索范式，显著加速了高质量启发式算法的生成，源代码可获取于此https URL。
英文摘要：
In this paper, we introduce ES-AHD, a novel framework that fundamentally integrates Evolution Strategy (ES) into Large Language Model (LLM)-driven Automatic Heuristic Design (AHD). Existing evolutionary approaches predominantly rely on random, individual-level mutation, leading to blind search and an imbalance between exploration and exploitation. To address these issues, ES-AHD introduces two core mechanisms. First, Semantic Recombination via LLMs discards traditional point-to-point reproduction. By leveraging the LLM's contextual reasoning to explicitly extract core insights from top-performing individuals, the algorithm establishes a promising semantic search direction. This transforms random code mutation into targeted, center-guided sampling inspired by ES. Second, Stochastic Covariance Adaptation via Temperature Sampling dynamically addresses the exploration-exploitation dilemma. By mapping the covariance matrix in ES to the LLM's sampling temperature, the framework employs a stochastic random walk mechanism with momentum. This approach primarily shrinks the search radius for micro-level code refinement, while retaining the critical ability to occasionally sample higher temperatures to escape semantic local optima. Ultimately, ES-AHD provides a highly directional, robust, and efficient search paradigm, significantly accelerating the generation of high-quality heuristic algorithms. The source code is available at: https://github.com/Mriya0306/ES-AHD.
