Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism

LLMs have demonstrated remarkable reasoning abilities, prompting interest in their application as black-box optimizers. This paper asserts that LLMs possess the capability for zero-shot optimization across diverse scenarios, including multi-objective and high-dimensional problems. We introduce a novel population-based method for numerical optimization using LLMs called Language-Model-Based Evolutionary Optimizer (LEO). Our hypothesis is supported through numerical examples, spanning benchmark and industrial engineering problems such as supersonic nozzle shape optimization, heat transfer, and windfarm layout optimization. We compare our method to several gradient-based and gradient-free optimization approaches. While LLMs yield comparable results to state-of-the-art methods, their imaginative nature and propensity to hallucinate demand careful handling. We provide practical guidelines for obtaining reliable answers from LLMs and discuss method limitations and potential research directions.