# QUBE: Enhancing Automatic Heuristic Design via Quality-Uncertainty Balanced Evolution

arXiv: https://arxiv.org/abs/2412.20694 · HTML: https://mlsanity.com/paper/2412.20694/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 30 Dec 2024.

## Builds on (most cited first, 12 of 12)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Language Model Crossover: Variation through Few-Shot Prompting](https://mlsanity.com/paper/2302.12170/) (2023)
- [LLMatic: Neural Architecture Search via Large Language Models and Quality Diversity Optimization](https://mlsanity.com/paper/2306.01102/) (2023)
- [Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism](https://mlsanity.com/paper/2403.02054/) (2024)
- [Deep Learning Assisted Heuristic Tree Search for the Container Pre-marshalling Problem](https://mlsanity.com/paper/1709.09972/) (2017)

## Built on by (most cited first, 5 of 5)

- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (2025)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [Using Reasoning Models to Generate Search Heuristics that Solve Open Instances of Combinatorial Design Problems](https://mlsanity.com/paper/2505.23881/) (2025)
- [An In-depth Study of LLM Contributions to the Bin Packing Problem](https://mlsanity.com/paper/2510.27353/) (2025)
- [PACE: Primitive-Aware Code Evolution for Automated Algorithm Design](https://mlsanity.com/paper/2608.07395/) (2026)

## Abstract (arXiv)

Solving NP-hard problems traditionally relies on heuristics, yet manually designing effective heuristics for complex problems remains a significant challenge. While recent advancements like FunSearch have shown that large language models (LLMs) can be integrated into evolutionary algorithms (EAs) for heuristic design, their potential is hindered by limitations in balancing exploitation and exploration. We introduce Quality-Uncertainty Balanced Evolution (QUBE), a novel approach that enhances LLM+EA methods by redefining the priority criterion within the FunSearch framework. QUBE employs the Quality-Uncertainty Trade-off Criterion (QUTC), based on our proposed Uncertainty-Inclusive Quality metric, to evaluate and guide the evolutionary process. Through extensive experiments on challenging NP-complete problems, QUBE demonstrates significant performance improvements over FunSearch and baseline methods. Our code are available at https://github.com/zzjchen/QUBE_code.