DGA₂D: Directed Graph-Guided Automated Algorithm Design with Large Language Models

DGA₂D is a framework for LLM-driven automated heuristic design that represents the open-ended program space as a directed graph. Nodes correspond to functional operators with multiple candidate code implementations, while directed walks form complete algorithmic pipelines. The framework introduces first-order path-dependent credit assignment, evaluating code variants according to their topological context rather than in isolation. The paper reports experiments on 12 combinatorial optimization problems spanning scheduling and routing, claiming up to a 10.96-percentage-point reduction in average normalized gap compared with state-of-the-art LLM baselines.