Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism

TL;DR

This paper presents LEO, a novel population-based optimization method leveraging Large Language Models' reasoning abilities for diverse numerical problems, demonstrating comparable results to existing methods with practical guidelines for reliability.

Contribution

Introduces LEO, a new LLM-based evolutionary optimizer for numerical problems, expanding the application of LLMs in optimization beyond traditional tasks.

Findings

LLMs can perform zero-shot optimization in various scenarios.

LEO achieves results comparable to state-of-the-art methods.

Practical guidelines improve reliability of LLM-based optimization.

Abstract

Large Language Models (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.