# CoupleEvo: Evolving Heuristics for Coupled Optimization Problems Using Large Language Models

arXiv: https://arxiv.org/abs/2605.06341 · HTML: https://mlsanity.com/paper/2605.06341/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 15 of 15)

- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [ShinkaEvolve: Towards Open-Ended And Sample-Efficient Program Evolution](https://mlsanity.com/paper/2509.19349/) (2025)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [HSEvo: Elevating Automatic Heuristic Design with Diversity-Driven Harmony Search and Genetic Algorithm Using LLMs](https://mlsanity.com/paper/2412.14995/) (2024)
- [A Systematic Survey on Large Language Models for Algorithm Design](https://mlsanity.com/paper/2410.14716/) (2024)
- [EvoX: Meta-Evolution for Automated Discovery](https://mlsanity.com/paper/2602.23413/) (2026)
- [EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design](https://mlsanity.com/paper/2508.03082/) (2025)
- [Efficient Heuristics Generation for Solving Combinatorial Optimization Problems Using Large Language Models](https://mlsanity.com/paper/2505.12627/) (2025)
- [HiFo-Prompt: Prompting with Hindsight and Foresight for LLM-based Automatic Heuristic Design](https://mlsanity.com/paper/2508.13333/) (2025)
- [G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design](https://mlsanity.com/paper/2602.08253/) (2026)
- [Solving the unit-load pre-marshalling problem in block stacking storage systems with multiple access directions](https://mlsanity.com/paper/2207.09118/) (2022)
- [Sorting multibay block stacking storage systems](https://mlsanity.com/paper/2405.04847/) (2024)
- [Large Neighborhood and Hybrid Genetic Search for Inventory Routing Problems](https://mlsanity.com/paper/2506.03172/) (2025)
- [Solve it with EASE](https://mlsanity.com/paper/2509.18108/) (2025)
- [Algorithmic Prompt-Augmentation for Efficient LLM-Based Heuristic Design for A* Search](https://mlsanity.com/paper/2601.19622/) (2026)

## Abstract (arXiv)

Many real-world optimization problems consist of multiple tightly coupled subproblems whose solutions must be coordinated to achieve high overall performance. However, existing large language model driven automated heuristic design approaches are limited to single-problem settings. In this paper, we propose CoupleEvo. CoupleEvo proposes three evolutionary coordination strategies to evolve heuristics for coupled optimization problems: the sequential strategy evolves heuristics for one subproblem after the other; the iterative strategy alternates the evolution of heuristics for different subproblems over successive generations; and the integrated strategy evolves heuristics for all problems simultaneously. The approach is evaluated on two representative coupled optimization problems. Experimental results show that decomposition-based strategies (sequential and iterative) provide more stable convergence and higher solution quality, while the integrated evolution strategy suffers from increased search complexity and variability. These findings highlight the importance of coordinating evolutionary search across interdependent subproblems and demonstrate the potential of LLM-driven heuristic design for complex coupled optimization problems. The code is available: https://github.com/tb-git-kit-research/CoupleEvo.