# MeEvo: Metacognitive Evolution Combined with Natural Evolution for Automatic Heuristic Design

arXiv: https://arxiv.org/abs/2606.14202 · HTML: https://mlsanity.com/paper/2606.14202/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [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)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [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)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [EvoPrompt: Connecting LLMs with Evolutionary Algorithms Yields Powerful Prompt Optimizers](https://mlsanity.com/paper/2309.08532/) (2023)
- [Monte Carlo Tree Search for Comprehensive Exploration in LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2501.08603/) (2025)
- [Metacognitive Prompting Improves Understanding in Large Language Models](https://mlsanity.com/paper/2308.05342/) (2023)
- [EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design](https://mlsanity.com/paper/2508.03082/) (2025)
- [Adaptive Tool Use in Large Language Models with Meta-Cognition Trigger](https://mlsanity.com/paper/2502.12961/) (2025)
- [Understanding the Importance of Evolutionary Search in Automated Heuristic Design with Large Language Models](https://mlsanity.com/paper/2407.10873/) (2024)
- [HiFo-Prompt: Prompting with Hindsight and Foresight for LLM-based Automatic Heuristic Design](https://mlsanity.com/paper/2508.13333/) (2025)
- [LLM-Driven Instance-Specific Heuristic Generation and Selection](https://mlsanity.com/paper/2506.00490/) (2025)
- [MeLA: A Metacognitive LLM-Driven Architecture for Automatic Heuristic Design](https://mlsanity.com/paper/2507.20541/) (2025)
- [Experience-Guided Reflective Co-Evolution of Prompts and Heuristics for Automatic Algorithm Design](https://mlsanity.com/paper/2509.24509/) (2025)
- [PyVRP^+: LLM-Driven Metacognitive Heuristic Evolution for Hybrid Genetic Search in Vehicle Routing Problems](https://mlsanity.com/paper/2604.07872/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have advanced Automatic Heuristic Design (AHD) by enabling heuristic generation through reasoning and code synthesis. In LLM-based AHD, the LLM reasons about algorithm design and generates executable heuristic code. Existing architectures adopt two main paradigms: Natural Evolution applies crossover and mutation to this code to explore diverse strategies, but discards the reasoning traces behind the design decisions, weakening knowledge retention; Metacognitive Evolution retains these reasoning traces and refines them through reflection, but lacks population-level recombination, limiting exploration. These limitations reduce search efficiency, stability, and solution quality on complex problems. To address this gap, we propose MeEvo, an AHD framework that cyclically couples Natural Evolution and Metacognitive Evolution with operator balance that shifts from exploration to exploitation. Natural Evolution explores heuristic code while recording LLM-generated reasoning traces, fitness values, errors and best heuristic into a shared history; Metacognitive Evolution then reflects on this history to generate improved heuristics that feed into the next Natural Evolution cycle. This design enables population-driven exploration and reflection-driven refinement to reinforce each other. Experiments on five optimization problems show that MeEvo achieves stronger performance and lower variance than tested LLM-based AHD architectures, especially on complex constrained tasks.