Open and closed source models for LLM-generated metaheuristics solving engineering optimization problem

Abstract

This paper explores the applicability of generative AI (genAI), specifically Large Language Models (LLMs), for the automatic generation and configuration of metaheuristic algorithms to address a real-world engineering problem: the optimal parameter estimation of time-delay systems in interconnected heating-cooling loops. The study introduces a pioneering workflow and iterative architecture with feedback within the emerging field of genAI-driven optimization for real optimization problems, eliminating the need for manually crafted or modified algorithms. This automated system empowers domain experts in engineering to solve complex optimization problems with minimal knowledge of optimization algorithms, lowering the barrier to entry for sophisticated algorithm use. We demonstrate how LLMs can generate effective optimizers under conditions like connstrained optimization problems where the solution lies near the boundaries of the search space. Four state-of-the-art LLMs (closed and open-sourced) have been selected for experiments. These are GPT-4o, GPT-4o mini, Claude Sonnet 3.5 and Llama 3.1. All studied LLMs generated metaheuristics that outperformed the initialization baseline optimization method (Random Search and CMA-ES). Notably, the Claude Sonnet 3.5 model generated a metaheuristic with the best mean results, almost matching the performance of the tuned state-of-the-art DISH algorithm, as an example of adaptive Differential Evolution.