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

2026-05-07

AI Summary

Current large language model (LLM)-driven approaches to automated heuristic design struggle to effectively solve complex optimization problems characterized by tightly coupled subproblems. This work proposes CoupleEvo, a novel framework that extends LLM-guided heuristic evolution to coupled optimization scenarios for the first time. It introduces three cooperative evolution strategies—sequential, iterative, and integrated—and systematically investigates how different coordination mechanisms affect search stability and solution quality. Experimental results on two representative classes of coupled optimization problems demonstrate that decomposition-based strategies (sequential and iterative) significantly outperform the integrated approach, exhibiting both more stable convergence behavior and superior solution quality.

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.

Problem

• coupled optimization problems
• heuristic design
• large language models
• evolutionary coordination
• interdependent subproblems

Innovation

• coupled optimization
• large language models
• evolutionary heuristics
• coordination strategies
• automated heuristic design