# ReVEL: Multi-Turn Reflective LLM-Guided Heuristic Evolution via Structured Performance Feedback

arXiv: https://arxiv.org/abs/2604.04940 · HTML: https://mlsanity.com/paper/2604.04940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [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)
- [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)
- [Continuous Chain of Thought Enables Parallel Exploration and Reasoning](https://mlsanity.com/paper/2505.23648/) (2025)
- [Explainable LLM Unlearning Through Reasoning](https://mlsanity.com/paper/2603.09980/) (2026)
- [From Heuristic Selection to Automated Algorithm Design: LLMs Benefit from Strong Priors](https://mlsanity.com/paper/2603.02792/) (2026)

## Abstract (arXiv)

Designing effective heuristics for NP-hard combinatorial optimization problems remains challenging and often requires substantial domain expertise. Recent LLM-guided evolutionary methods have shown promise for automated heuristic generation, but most existing approaches refine heuristics independently or through limited pairwise feedback. We propose ReVEL: Multi-Turn Reflective LLM-Guided Heuristic Evolution via Structured Performance Feedback, a framework for group-wise multi-turn heuristic refinement. ReVEL organizes heuristics into behavior-aware reflective groups, including similarity-driven groups for localized refinement and diversity-driven groups for exploratory search. Within each group, the LLM performs iterative multi-turn refinement using accumulated performance feedback, enabling related heuristics to be jointly analyzed and progressively improved across evolutionary iterations. Experiments on standard combinatorial optimization benchmarks show that ReVEL generally improves optimization performance over existing LLM-guided evolutionary baselines across multiple settings and LLM backbones. Additional analyses suggest that behavior-aware grouping contributes to more consistent refinement trajectories during iterative heuristic evolution.