Organizations: School of Automation Science and Electrical Engineering, Beihang University, Beijing, China · School of Computer Science and Engineering, Beihang University, Beijing, China
Abstract
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 DGA2D. 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 DGA2D. It reduces the average normalized gap by up to 10.96 percentage points compared to state-of-the-art LLM baselines.
Designing heuristics for combinatorial optimization problems (COPs) is a fundamental yet challenging task that traditionally requires extensive domain expertise. Recently, Large Language Model (LLM)-based Automated Heuristic Design (AHD) has shown promise in autonomously generating heuristic components with minimal human intervention. However, most existing LLM-based AHD methods enforce fixed algorithmic templates to ensure executability, which confines the search to component-level tuning and limits system-level algorithmic expressiveness. To enable open-ended solver synthesis beyond rigid templates, we propose Automated Algorithm Design via Evolutionary Program Trees (A2DEPT), which treats LLMs as system-level algorithm architects. A2DEPT explores the vast program space via a tree-structured evolutionary search with hybrid selection and hierarchical operators, enabling iterative refinement of complete algorithms. To make open-ended generation practical, we enforce executability with a lightweight program-maintenance loop that performs feedback-driven repair. In experiments, A2DEPT consistently outperforms representative LLM-based baselines on both standard and highly constrained benchmarks. On the standard benchmarks, it reduces the mean normalized optimality gap by 9.8% relative to the strongest competing AHD baseline.
Large language models (LLMs) have emerged as powerful tools for automatic algorithm design (AAD). However, existing pipelines remain inefficient. They operate at the granularity of full algorithms, redundantly rewriting recurring substructures and discarding low-fitness candidates that may contain valuable algorithmic features. We formalize budget-efficient automatic algorithm design, wherein the search policy maximizes realized fitness subject to limited computational cost. We propose a directed acyclic graph representation of algorithms and build a search framework that fully exploits the LLM's output. Instead of querying the LLM for full algorithms, we use it to obtain corrections: compact operators that add, replace, or remove code blocks. Each correction augments the graph, yielding new algorithms that compose with prior corrections. This graph structure decomposes algorithms into sets of corrections, enabling correction-level credit assignment that informs subsequent queries. We complement this framework with theoretical insights into the ideal balance between search depth and breadth at different budget levels. We validate our method empirically on three combinatorial optimization problems, demonstrating consistent superiority of our graph-based search over full-algorithm search at equal token budget. Finally, our experiments suggest that rich contexts help only when the LLM's prior knowledge is shallow, and can hinder performance otherwise.
Automatic heuristic design (AHD) has emerged as a promising paradigm for solving NP-hard combinatorial optimization problems (COPs). Recent works show that large language models (LLMs), when integrated into well-designed frameworks (i.e., LLM-AHD), can autonomously discover high-performing heuristics. However, existing LLM-AHD frameworks typically treat LLMs as passive generators within fixed workflows, where the model generates heuristics from manually designed, limited context. Such context may fail to capture state-dependent information (e.g., specific failure modes), leading to inefficient trial-and-error exploration. To overcome these limitations, we propose AHD Agent, a novel tool-integrated, multi-turn framework that empowers LLMs to proactively decide whether to generate heuristics or invoke tools to retrieve targeted evidence from the solving environment. To effectively train such a dynamic decision-making agent, we introduce an agentic reinforcement learning (RL) system, which leverages a novel environment synthesis pipeline to optimize a compact model's generalizable AHD capabilities. Experiments across eight diverse domains, including four held-out tasks, demonstrate that our 4B-parameter agent matches or surpasses state-of-the-art baselines using much larger models, while requiring significantly fewer evaluations. Model and inference scaling analysis further reveals that AHD Agent offers an effective trajectory toward truly autonomous heuristic design.