Evolutionary algorithms (EAs) have achieved remarkable success in tackling complex combinatorial optimization problems. However, EAs often demand carefully-designed operators with the aid of domain expertise to achieve satisfactory performance. In this work, we present the first study on large language models (LLMs) as evolutionary combinatorial optimizers. The main advantage is that it requires minimal domain knowledge and human efforts, as well as no additional training of the model. This approach is referred to as LLM-driven EA (LMEA). Specifically, in each generation of the evolutionary search, LMEA instructs the LLM to select parent solutions from current population, and perform crossover and mutation to generate offspring solutions. Then, LMEA evaluates these new solutions and include them into the population for the next generation. LMEA is equipped with a self-adaptation mechanism that controls the temperature of the LLM. This enables it to balance between exploration and exploitation and prevents the search from getting stuck in local optima. We investigate the power of LMEA on the classical traveling salesman problems (TSPs) widely used in combinatorial optimization research. Notably, the results show that LMEA performs competitively to traditional heuristics in finding high-quality solutions on TSP instances with up to 20 nodes. Additionally, we also study the effectiveness of LLM-driven crossover/mutation and the self-adaptation mechanism in evolutionary search. In summary, our results reveal the great potentials of LLMs as evolutionary optimizers for solving combinatorial problems. We hope our research shall inspire future explorations on LLM-driven EAs for complex optimization challenges.

翻译：进化算法（EAs）在解决复杂组合优化问题方面取得了显著成功。然而，进化算法通常需要借助领域专业知识精心设计的算子才能获得令人满意的性能。在这项工作中，我们首次研究了将大语言模型（LLMs）作为进化组合优化器。其主要优势在于所需领域知识和人工干预极少，且无需对模型进行额外训练。该方法被称为LLM驱动的进化算法（LMEA）。具体而言，在进化搜索的每一代中，LMEA指导LLM从当前种群中选择父代解，并执行交叉和变异操作以生成子代解。随后，LMEA评估这些新解并将其纳入下一代种群。LMEA配备了一种控制LLM温度的自适应机制，从而能够平衡探索与利用，避免搜索陷入局部最优。我们以组合优化研究中广泛使用的经典旅行商问题（TSPs）为例，考察了LMEA的能力。结果显示，在节点数不超过20的TSP实例上，LMEA在寻找高质量解方面与传统启发式方法相比具有竞争力。此外，我们还研究了LLM驱动的交叉/变异以及进化搜索中自适应机制的有效性。总之，我们的结果揭示了LLMs作为进化优化器解决组合问题的巨大潜力。我们希望这项研究能推动未来对LLM驱动的进化算法在复杂优化挑战中的探索。