Improving Existing Optimization Algorithms with LLMs

The integration of Large Language Models (LLMs) into optimization has created a powerful synergy, opening exciting research opportunities. This paper investigates how LLMs can enhance existing optimization algorithms. Using their pre-trained knowledge, we demonstrate their ability to propose innovative heuristic variations and implementation strategies. To evaluate this, we applied a non-trivial optimization algorithm, Construct, Merge, Solve and Adapt (CMSA) -- a hybrid metaheuristic for combinatorial optimization problems that incorporates a heuristic in the solution construction phase. Our results show that an alternative heuristic proposed by GPT-4o outperforms the expert-designed heuristic of CMSA, with the performance gap widening on larger and denser graphs. Project URL:this https URL

@article{sartori2025_2502.08298,
  title={ Improving Existing Optimization Algorithms with LLMs },
  author={ Camilo Chacón Sartori and Christian Blum },
  journal={arXiv preprint arXiv:2502.08298},
  year={ 2025 }
}