DGA₂D：基于有向图的大语言模型驱动自动化算法设计
DGA$_2$D: Directed Graph-Guided Automated Algorithm Design with Large Language Models
浏览论文内容
中文总结 AI 辅助
该研究针对LLM驱动自动化算法设计的现有局限，提出DGA₂D框架，通过有向图建模程序空间与一阶路径依赖信用分配机制，在12种组合优化问题上使平均归一化间隙最多降低10.96个百分点。
中文摘要 AI 辅助
大语言模型（LLMs）的快速发展为求解NP难组合优化问题（COPs）的启发式自动化设计（AHD）开辟了新途径。然而，现有LLM驱动的AHD方法大多局限于僵化的求解器模板，将搜索过程限制在孤立的模块调优中。转向完全自主的系统级算法设计至关重要，但面临生成算子可靠性低、搜索空间极大、信用分配无效等难题。为克服这些缺陷，本文提出了一种基于有向图的自动化算法设计框架，命名为DGA₂D。该框架将开放的程序空间构建为有向图，每个节点代表一个功能算子，可通过多个候选代码实现实例化，而有向路径则构成完整的算法流程。本文引入了一种一阶路径依赖信用分配机制，严格基于拓扑上下文评估代码变体。在12种不同的COPs（涵盖从复杂调度到路由的各类问题）上开展的大量实验表明，DGA₂D具有稳定的经验优势，与最先进的LLM基线相比，其平均归一化间隙最多降低10.96个百分点。
英文摘要
The rapid development of Large Language Models (LLMs) has opened new avenues for Automated Heuristic Design (AHD) for solving NP-hard combinatorial optimization problems (COPs). However, existing LLM-driven AHD methods are largely confined to rigid solver templates, relegating the search process to isolated module tuning. Transitioning to fully autonomous, system-level algorithm design is essential but fraught with low reliability of generated operators, extremely large search spaces, and ineffective credit assignment. To overcome these drawbacks, this paper proposes a Directed Graph-Guided Automated Algorithm Design framework, termed DGA$_2$D. It structures the open-ended program space as a directed graph, where each node represents a functional operator that can be instantiated using one of multiple candidate code implementations, while directed walks constitute complete algorithmic pipelines. A first-order path-dependent credit assignment mechanism is introduced to evaluate code variations strictly based on their topological context. Extensive experiments across 12 distinct COPs, ranging from complex scheduling to routing, demonstrate the consistent empirical advantages of DGA$_2$D. It reduces the average normalized gap by up to 10.96 percentage points compared to state-of-the-art LLM baselines.
