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

2026-06-12

AI Summary

Existing large language model (LLM)-driven approaches to automated heuristic design often suffer from insufficient solution efficiency and stability on complex optimization problems due to imbalanced exploration–exploitation trade-offs, limited knowledge transfer across iterations, and premature convergence. To address these limitations, this work proposes MeEvo, a dual-layer evolutionary framework that organically integrates natural evolution with metacognitive evolution for the first time. The natural evolution layer employs genetic operators to explore heuristic code while recording reasoning trajectories, whereas the metacognitive layer leverages shared historical data to reflectively generate improved strategies and feed them back into the population. This closed-loop architecture synergistically combines LLM-based code generation with reflective prompting, enabling collaborative enhancement between population-level exploration and individual-level refinement. Experimental results demonstrate that MeEvo significantly outperforms state-of-the-art methods across five optimization tasks, exhibiting superior performance and robustness, particularly in scenarios with complex constraints.

Abstract

Large Language Models (LLMs) have advanced Automatic Heuristic Design (AHD) by enabling heuristic generation through reasoning and code synthesis. Existing LLM-based AHD architectures mainly follow two paradigms: Natural Evolution, which uses crossover and mutation to explore heuristic programs, and Metacognitive Evolution, which refines reasoning through reflection. However, Natural Evolution discards reasoning traces, weakening knowledge inheritance and exploitation, while Metacognitive Evolution lacks population-level recombination, limiting exploration and increasing the risk of premature convergence. These limitations reduce search efficiency, stability, and solution quality on complex problems. To address this gap, we propose MeEvo, a dual-layer AHD framework that cyclically couples Natural Evolution and Metacognitive Evolution. Natural Evolution explores heuristic code while recording reasoning traces, fitness values, and errors into a shared history; Metacognitive Evolution then reflects on this history to generate improved heuristics that re-enter the parent pool for the next cycle. This design enables population-driven exploration and reflection-driven refinement to reinforce each other. Experiments on five optimization problems with two LLM backbones show that MeEvo achieves stronger and more stable performance than existing LLM-based AHD architectures, especially on complex constrained tasks.

Problem

• Automatic Heuristic Design
• Natural Evolution
• Metacognitive Evolution
• Large Language Models
• Premature Convergence

Innovation

• Metacognitive Evolution
• Natural Evolution
• Automatic Heuristic Design
• Large Language Models
• Evolutionary Optimization