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，EAs 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型语言模型（LLMs）作为进化组合优化器。其主要优势在于只需最少的领域知识和人力投入，且无需对模型进行额外训练。该方法被称为 LLM 驱动的 EA（LMEA）。具体而言，在进化搜索的每一代中，LMEA 指示 LLM 从当前种群中选择父代解，并执行交叉和变异以生成子代解。然后，LMEA 评估这些新解并将其纳入下一代的种群中。LMEA 配备了一种控制 LLM 温度的自适应机制，使其能够平衡探索与开发，并防止搜索陷入局部最优。我们在组合优化研究中广泛使用的经典旅行商问题（TSPs）上探究了 LMEA 的能力。值得注意的是，结果表明，在节点数最多为 20 的 TSP 实例上，LMEA 在寻找高质量解方面与传统启发式方法具有竞争力。此外，我们还研究了 LLM 驱动的交叉/变异以及自适应机制在进化搜索中的有效性。总之，我们的结果揭示了 LLM 作为进化优化器在解决组合问题方面的巨大潜力。我们希望这项研究能够激发未来关于 LLM 驱动的 EA 在复杂优化挑战中的探索。