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

TL;DR

CoupleEvo introduces three evolutionary strategies to develop heuristics for complex coupled optimization problems, demonstrating the effectiveness of decomposition-based methods over integrated evolution, with code available online.

Contribution

This paper presents novel evolutionary coordination strategies for heuristics in coupled optimization, leveraging large language models for complex problem solving.

Findings

Decomposition strategies yield more stable convergence.

Sequential and iterative strategies outperform integrated evolution.

Code implementation is publicly available at the provided GitHub link.

Abstract

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.