ES-AHD: An Evolution Strategy Framework for Automatic Heuristic Design

2026-08-26

AI Summary

本文提出ES-AHD框架，通过语义重组和随机协方差适应解决自动启发式设计中的盲目搜索和探索-利用不平衡问题。

Abstract

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.

Problem

• Evolution Strategy
• Automatic Heuristic Design
• Exploration-Exploitation Dilemma
• Large Language Model

Innovation

• Evolution Strategy
• Semantic Recombination
• Stochastic Covariance Adaptation
• Temperature Sampling