# BEAM: Bi-level Memory-adaptive Algorithmic Evolution for LLM-Powered Heuristic Design

arXiv: https://arxiv.org/abs/2604.12898 · HTML: https://mlsanity.com/paper/2604.12898/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 72 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 30 of 39)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (2023)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [A Systematic Survey of Prompt Engineering in Large Language Models: Techniques and Applications](https://mlsanity.com/paper/2402.07927/) (2024)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [OptiMUS: Scalable Optimization Modeling with (MI)LP Solvers and Large Language Models](https://mlsanity.com/paper/2402.10172/) (2024)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [Understanding LSTM -- a tutorial into Long Short-Term Memory Recurrent Neural Networks](https://mlsanity.com/paper/1909.09586/) (2019)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap](https://mlsanity.com/paper/2401.10034/) (2024)
- [DebugBench: Evaluating Debugging Capability of Large Language Models](https://mlsanity.com/paper/2401.04621/) (2024)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization](https://mlsanity.com/paper/2406.01661/) (2024)
- [Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning](https://mlsanity.com/paper/2504.05108/) (2025)
- [Cost-aware Bayesian Optimization](https://mlsanity.com/paper/2003.10870/) (2020)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Zero Bubble Pipeline Parallelism](https://mlsanity.com/paper/2401.10241/) (2023)
- [Finding Near-Optimal Independent Sets at Scale](https://mlsanity.com/paper/1509.00764/) (2015)
- [LLM4AD: A Platform for Algorithm Design with Large Language Model](https://mlsanity.com/paper/2412.17287/) (2024)
- [In-the-loop Hyper-Parameter Optimization for LLM-Based Automated Design of Heuristics](https://mlsanity.com/paper/2410.16309/) (2024)
- [Outline, Then Details: Syntactically Guided Coarse-To-Fine Code Generation](https://mlsanity.com/paper/2305.00909/) (2023)
- [Large Language Models for Code Generation: A Comprehensive Survey of Challenges, Techniques, Evaluation, and Applications](https://mlsanity.com/paper/2503.01245/) (2025)

## Built on by (most cited first, 1 of 1)

- [PACE: Primitive-Aware Code Evolution for Automated Algorithm Design](https://mlsanity.com/paper/2608.07395/) (2026)

## Abstract (arXiv)

Large Language Model-based Hyper Heuristic (LHH) has recently emerged as an efficient way for automatic heuristic design. However, most existing LHHs just perform well in optimizing a single function within a pre-defined solver. Their single-layer evolution makes them not effective enough to write a competent complete solver. While some variants incorporate hyperparameter tuning or attempt to generate complex code through iterative local modifications, they still lack a high-level algorithmic modeling, leading to limited exploration efficiency. To address this, we reformulate heuristic design as a Bi-level Optimization problem and propose BEAM (Bi-level Memory-adaptive Algorithmic Evolution). BEAM's exterior layer evolves high-level algorithmic structures with function placeholders through genetic algorithm (GA), while the interior layer realizes these placeholders via Monte Carlo Tree Search (MCTS). We further introduce an Adaptive Memory module to facilitate complex code generation. To support the evaluation for complex code generation, we point out the limitations of starting LHHs from scratch or from code templates and introduce a Knowledge Augmentation (KA) Pipeline. Experimental results on several optimization problems demonstrate that BEAM significantly outperforms existing LHHs, notably reducing the optimality gap by 37.84% on aggregate in CVRP hybrid algorithm design. BEAM also designs a heuristic that outperforms SOTA Maximum Independent Set (MIS) solver KaMIS.