Improving Existing Optimization Algorithms with LLMs

TL;DR

This paper explores how Large Language Models can enhance optimization algorithms by proposing innovative heuristics, demonstrated through GPT-4o outperforming expert heuristics in a hybrid metaheuristic for combinatorial problems.

Contribution

It introduces a method for leveraging LLMs to generate and improve heuristics within existing optimization algorithms, showcasing significant performance gains.

Findings

GPT-4o outperforms expert heuristics in CMSA

Performance gap widens on larger, denser graphs

LLMs can propose effective heuristic variations

Abstract

The integration of Large Language Models (LLMs) into optimization has created a powerful synergy, opening exciting research opportunities. This paper investigates how LLMs can enhance existing optimization algorithms. Using their pre-trained knowledge, we demonstrate their ability to propose innovative heuristic variations and implementation strategies. To evaluate this, we applied a non-trivial optimization algorithm, Construct, Merge, Solve and Adapt (CMSA) -- a hybrid metaheuristic for combinatorial optimization problems that incorporates a heuristic in the solution construction phase. Our results show that an alternative heuristic proposed by GPT-4o outperforms the expert-designed heuristic of CMSA, with the performance gap widening on larger and denser graphs. Project URL: https://imp-opt-algo-llms.surge.sh/