# ACEvo: Adversarial Co-Evolution of Problem Distributions and Solvers for Combinatorial Optimization

arXiv: https://arxiv.org/abs/2506.02594 · HTML: https://mlsanity.com/paper/2506.02594/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 50 references that are in the map.
- First posted on arXiv 3 Jun 2025.

## Builds on (most cited first, 26 of 26)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [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)
- [Large Language Models as Commonsense Knowledge for Large-Scale Task Planning](https://mlsanity.com/paper/2305.14078/) (2023)
- [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)
- [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)
- [Unleashing the Potential of Large Language Models as Prompt Optimizers: Analogical Analysis with Gradient-based Model Optimizers](https://mlsanity.com/paper/2402.17564/) (2024)
- [FastMAC: Stochastic Spectral Sampling of Correspondence Graph](https://mlsanity.com/paper/2403.08770/) (2024)
- [Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)](https://mlsanity.com/paper/1910.04966/) (2019)
- [Planning of Heuristics: Strategic Planning on Large Language Models with Monte Carlo Tree Search for Automating Heuristic Optimization](https://mlsanity.com/paper/2502.11422/) (2025)
- [Large Language Models Powered Context-aware Motion Prediction in Autonomous Driving](https://mlsanity.com/paper/2403.11057/) (2024)
- [Planning Assembly Sequence with Graph Transformer](https://mlsanity.com/paper/2210.05236/) (2022)
- [Large Language Models for Combinatorial Optimization of Design Structure Matrix](https://mlsanity.com/paper/2411.12571/) (2024)
- [Heuristics for Vehicle Routing Problem: A Survey and Recent Advances](https://mlsanity.com/paper/2303.04147/) (2023)
- [Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimization](https://mlsanity.com/paper/2501.11968/) (2025)
- [Leveraging Large Language Models to Develop Heuristics for Emerging Optimization Problems](https://mlsanity.com/paper/2503.03350/) (2025)
- [Improving Existing Optimization Algorithms with LLMs](https://mlsanity.com/paper/2502.08298/) (2025)

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

- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [Game-Theoretic Co-Evolution for LLM-Based Heuristic Discovery](https://mlsanity.com/paper/2601.22896/) (2026)
- [RAISE: LLM-based Automated Heuristic Design with Robust Adversary Instance Search](https://mlsanity.com/paper/2606.31801/) (2026)
- [MOSAIC: Adversarial Co-evolution of Specialist Heuristics and Problem Instances for LLM-based Automated Heuristic Design](https://mlsanity.com/paper/2608.07544/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used to synthesize heuristic programs, yet most existing pipelines optimize solvers against fixed benchmark distributions. This static setup can obscure solver weaknesses and limit understanding of how LLM-designed algorithms adapt under distribution shift. We present Adversarial Co-Evolution (ACEvo), a closed-loop framework in which LLMs iteratively co-evolve two types of executable programs: heuristic solvers and problem generators. The generator proposes increasingly challenging instances, while the solver is refined to improve performance on the evolving distribution, forming an automated adversarial curriculum for program design and evaluation. We instantiate ACEvo on routing problems, including TSP, OP, and CVRP. Across these domains, the framework produces instance distributions that consistently induce larger optimality gaps than standard benchmarks and yields solver programs that outperform those obtained from static-training baselines under distribution shift. Beyond final performance, ACEvo provides a testbed for studying LLM-based algorithm design under evolving distributions, including how reflective mutation, adversarial feedback, and co-adaptation shape the evolution of both generators and solvers. These results suggest that closed-loop co-evolution is a promising paradigm for using language models not only to generate algorithms, but also to construct adaptive evaluation environments.