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

Researchers have introduced CoupleEvo, a novel framework designed to address the limitations of existing Large Language Model (LLM)-driven automated heuristic design approaches, which are typically restricted to single-problem settings. Real-world optimization often involves multiple tightly coupled subproblems requiring coordinated solutions. CoupleEvo proposes three evolutionary coordination strategies: sequential, iterative, and integrated. The sequential strategy evolves heuristics for subproblems one after another, while the iterative strategy alternates evolution across successive generations. The integrated strategy attempts to evolve heuristics for all problems simultaneously. Evaluated on two representative coupled optimization problems, experimental results indicate that decomposition-based strategies (sequential and iterative) offer more stable convergence and higher solution quality. In contrast, the integrated strategy suffers from increased search complexity and variability. These findings underscore the critical importance of coordinating evolutionary search across interdependent subproblems. The study demonstrates the significant potential of LLM-driven heuristic design for complex, coupled optimization challenges. The associated code has been made publicly available to facilitate further research and application in this domain.