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

arXiv: https://arxiv.org/abs/2608.00700 · HTML: https://mlsanity.com/paper/2608.00700/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 1 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimization](https://mlsanity.com/paper/2502.02941/) (2025)
- [Solving a New 3D Bin Packing Problem with Deep Reinforcement Learning Method](https://mlsanity.com/paper/1708.05930/) (2017)
- [ConfigX: Modular Configuration for Evolutionary Algorithms via Multitask Reinforcement Learning](https://mlsanity.com/paper/2412.07507/) (2024)
- [Learning from Offline and Online Experiences: A Hybrid Adaptive Operator Selection Framework](https://mlsanity.com/paper/2404.10252/) (2024)
- [AC-Band: A Combinatorial Bandit-Based Approach to Algorithm Configuration](https://mlsanity.com/paper/2212.00333/) (2022)
- [A2DEPT: Large Language Model-Driven Automated Algorithm Design via Evolutionary Program Trees](https://mlsanity.com/paper/2604.24043/) (2026)
- [RESCHED: Rethinking Flexible Job Shop Scheduling from a Transformer-based Architecture with Simplified States](https://mlsanity.com/paper/2603.07020/) (2026)

## Abstract (arXiv)

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.