# DyACE: Dynamic Algorithm Co-evolution for Online Automated Heuristic Design with Large Language Model

arXiv: https://arxiv.org/abs/2603.13344 · HTML: https://mlsanity.com/paper/2603.13344/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 7 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [Eureka: Human-Level Reward Design via Coding Large Language Models](https://mlsanity.com/paper/2310.12931/) (2023)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (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)
- [Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learning](https://mlsanity.com/paper/2010.12367/) (2020)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [ParamILS: An Automatic Algorithm Configuration Framework](https://mlsanity.com/paper/1401.3492/) (2014)
- [LLMatic: Neural Architecture Search via Large Language Models and Quality Diversity Optimization](https://mlsanity.com/paper/2306.01102/) (2023)
- [Evolving Code with A Large Language Model](https://mlsanity.com/paper/2401.07102/) (2024)
- [CALM: Co-evolution of Algorithms and Language Model for Automatic Heuristic Design](https://mlsanity.com/paper/2505.12285/) (2025)
- [CoCoEvo: Co-Evolution of Programs and Test Cases to Enhance Code Generation](https://mlsanity.com/paper/2502.10802/) (2025)
- [Automatic programming via large language models with population self-evolution for dynamic fuzzy job shop scheduling problem](https://mlsanity.com/paper/2410.22657/) (2024)

## Abstract (arXiv)

The prevailing paradigm in Automated Heuristic Design (AHD) typically relies on the assumption that a single, fixed algorithm can effectively navigate the shifting dynamics of a combinatorial search. This static approach often proves inadequate for Perturbative Heuristics, where the optimal algorithm for escaping local optima depends heavily on the specific search phase. To address this limitation, we reformulate heuristic design as a Non-stationary Bi-level Control problem and introduce DyACE (Dynamic Algorithm Co-evolution). Distinct from standard open-loop solvers, DyACE use a Receding Horizon Control architecture to continuously co-evolve the heuristic logic alongside the solution population. A core element of this framework is the Look-Ahead Rollout Search, which queries the landscape geometry to extract Search Trajectory Features. This sensory feedback allows the Large Language Model (LLM) to function as a grounded meta-controller, prescribing phase-specific interventions tailored to the real-time search status. We validate DyACE on three representative combinatorial optimization benchmarks. The results demonstrate that our method significantly outperforms state-of-the-art static baselines, exhibiting superior scalability in high-dimensional search spaces. Furthermore, ablation studies confirm that dynamic adaptation fails without grounded perception, often performing worse than static algorithms. This indicates that DyACE's effectiveness stems from the causal alignment between the synthesized logic and the verified gradients of the optimization landscape.