# CALM: Co-evolution of Algorithms and Language Model for Automatic Heuristic Design

arXiv: https://arxiv.org/abs/2505.12285 · HTML: https://mlsanity.com/paper/2505.12285/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2025.

## Built on by (most cited first, 29 of 29)

- [EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design](https://mlsanity.com/paper/2508.03082/) (2025)
- [HiFo-Prompt: Prompting with Hindsight and Foresight for LLM-based Automatic Heuristic Design](https://mlsanity.com/paper/2508.13333/) (2025)
- [Glia: A Human-Inspired AI for Automated Systems Design and Optimization](https://mlsanity.com/paper/2510.27176/) (2025)
- [VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems](https://mlsanity.com/paper/2510.07073/) (2025)
- [G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2602.08253/) (2026)
- [Improving Coherence and Persistence in Agentic AI for System Optimization](https://mlsanity.com/paper/2603.21321/) (2026)
- [LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regression](https://mlsanity.com/paper/2505.18602/) (2025)
- [Fine-tuning Large Language Model for Automated Algorithm Design](https://mlsanity.com/paper/2507.10614/) (2025)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [MeLA: A Metacognitive LLM-Driven Architecture for Automatic Heuristic Design](https://mlsanity.com/paper/2507.20541/) (2025)
- [Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLM](https://mlsanity.com/paper/2510.11121/) (2025)
- [AHD Agent: Agentic Reinforcement Learning for Automatic Heuristic Design](https://mlsanity.com/paper/2605.08756/) (2026)
- [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)
- [MCCE: A Framework for Multi-LLM Collaborative Search in Discrete Spaces with Similarity-Filtered Preference Learning](https://mlsanity.com/paper/2510.06270/) (2025)
- [Algorithmic Prompt-Augmentation for Efficient LLM-Based Heuristic Design for A* Search](https://mlsanity.com/paper/2601.19622/) (2026)
- [ATLAS: Scaffold-Free Algorithm Synthesis by LLMs via Embedding-Guided Quality-Diversity Search](https://mlsanity.com/paper/2608.15546/) (2026)
- [Language-Guided Tuning: Configuration Optimization for Automated ML Research](https://mlsanity.com/paper/2508.15757/) (2025)
- [Using Multi-modal Large Language Model to Boost Fireworks Algorithm's Ability in Settling Challenging Optimization Tasks](https://mlsanity.com/paper/2511.03137/) (2025)
- [Heuristic Search as Language-Guided Program Optimization](https://mlsanity.com/paper/2602.16038/) (2026)
- [DyACE: Dynamic Algorithm Co-evolution for Online Automated Heuristic Design with Large Language Model](https://mlsanity.com/paper/2603.13344/) (2026)
- [MOSAIC: Adversarial Co-evolution of Specialist Heuristics and Problem Instances for LLM-based Automated Heuristic Design](https://mlsanity.com/paper/2608.07544/) (2026)
- [LLM-Driven Algorithm Design for Quantum Circuit Synthesis based on Binary Decision Diagrams](https://mlsanity.com/paper/2609.05327/) (2026)
- [SPO: Discovering Adaptive Large Neighborhood Search Operators via Stackelberg Program Optimization](https://mlsanity.com/paper/2609.31179/) (2026)
- [LLMs as Adaptive Meta-Solvers: Strategy-Diverse RL for Industrial-Scale Optimization](https://mlsanity.com/paper/2609.34427/) (2026)
- [SimpleEvol: An Agent-Loop Framework for LLM-Driven Automated Heuristic Design with Minimal Human Priors](https://mlsanity.com/paper/2609.37172/) (2026)
- [From Search to Signal: Online Post-Training in Automatic Heuristic Design](https://mlsanity.com/paper/2609.39383/) (2026)
- [TRACE: Tackling Real-World Resource Assignment Problems via Agentic Heuristic Design](https://mlsanity.com/paper/2610.01887/) (2026)
- [EPOCH: Coverage-Aware Evolution with Experiential Preference Optimization for LLM-based Automated Heuristic Design](https://mlsanity.com/paper/2610.17379/) (2026)

## Abstract (arXiv)

Tackling complex optimization problems often relies on expert-designed heuristics, typically crafted through extensive trial and error. Recent advances demonstrate that large language models (LLMs), when integrated into well-designed evolutionary search frameworks, can autonomously discover high-performing heuristics at a fraction of the traditional cost. However, existing approaches predominantly rely on verbal guidance, i.e., manipulating the prompt generation process, to steer the evolution of heuristics, without adapting the underlying LLM. We propose a hybrid framework that combines verbal and numerical guidance, the latter achieved by fine-tuning the LLM via reinforcement learning based on the quality of generated heuristics. This joint optimization allows the LLM to co-evolve with the search process. Our method outperforms state-of-the-art (SOTA) baselines across various optimization tasks, running locally on a single 24GB GPU using a 7B model with INT4 quantization. It surpasses methods that rely solely on verbal guidance, even when those use significantly more powerful API-based models.