# Experience-Guided Reflective Co-Evolution of Prompts and Heuristics for Automatic Algorithm Design

arXiv: https://arxiv.org/abs/2509.24509 · HTML: https://mlsanity.com/paper/2509.24509/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 35 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [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)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/1911.09539/) (2019)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [Large Language Models As Evolution Strategies](https://mlsanity.com/paper/2402.18381/) (2024)
- [Multi-objective Evolution of Heuristic Using Large Language Model](https://mlsanity.com/paper/2409.16867/) (2024)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [MetaBox: A Benchmark Platform for Meta-Black-Box Optimization with Reinforcement Learning](https://mlsanity.com/paper/2310.08252/) (2023)
- [How Good Is Neural Combinatorial Optimization? A Systematic Evaluation on the Traveling Salesman Problem](https://mlsanity.com/paper/2209.10913/) (2022)
- [Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization](https://mlsanity.com/paper/2310.15196/) (2023)
- [G4SATBench: Benchmarking and Advancing SAT Solving with Graph Neural Networks](https://mlsanity.com/paper/2309.16941/) (2023)
- [RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization](https://mlsanity.com/paper/2503.16159/) (2025)
- [Large Language Models and Evolutionary Computation: A Critical Review of Bidirectional Interaction, Automated Algorithm Design, and Co-Adaptive Systems](https://mlsanity.com/paper/2505.15741/) (2025)

## Built on by (most cited first, 4 of 4)

- [Game-Theoretic Co-Evolution for LLM-Based Heuristic Discovery](https://mlsanity.com/paper/2601.22896/) (2026)
- [RefineEvo: Planning-Guided Heuristic Evolution with Bidirectional Experience](https://mlsanity.com/paper/2607.11358/) (2026)
- [HMACE: Heterogeneous Multi-Agent Collaborative Evolution for Combinatorial Optimization](https://mlsanity.com/paper/2605.07214/) (2026)
- [MeEvo: Metacognitive Evolution Combined with Natural Evolution for Automatic Heuristic Design](https://mlsanity.com/paper/2606.14202/) (2026)

## Abstract (arXiv)

Combinatorial optimization problems are traditionally tackled with handcrafted heuristic algorithms, which demand extensive domain expertise and significant implementation effort. Recent progress has highlighted the potential of automatic heuristics design powered by large language models (LLMs), enabling the automatic generation and refinement of heuristics. These approaches typically maintain a population of heuristics and employ LLMs as mutation operators to evolve them across generations. While effective, such methods often risk stagnating in local optima. To address this issue, we propose the Experience-Guided Reflective Co-Evolution of Prompt and Heuristics (EvoPH) for automatic algorithm design, a novel framework that integrates the island migration model with the elites selection algorithm to simulate diverse heuristics populations. In EvoPH, prompts are co-evolved with heuristic algorithms, guided by performance feedback. We evaluate our framework on two problems, i.e., Traveling Salesman Problem and Bin Packing Problem. Experimental results demonstrate that EvoPH achieves the lowest relative error against optimal solutions across both datasets, advancing the field of automatic algorithm design with LLMs.