Multi-Objective Hierarchical Optimization with Large Language Models

TL;DR

This paper introduces a hierarchical optimization method using large language models as surrogate models, which adaptively partitions the input space to efficiently find solutions close to the true Pareto set, outperforming some existing methods.

Contribution

It presents a novel hierarchical search strategy leveraging LLMs for multi-objective optimization, focusing on local reasoning within partitioned sub-spaces to improve convergence and efficiency.

Findings

Algorithm converges to true Pareto set under regularity assumptions.

Outperforms global LLM-based optimizer in experiments.

Matches the performance of standard evolutionary and Bayesian methods.

Abstract

Despite their widespread adoption in various domains, especially due to their powerful reasoning capabilities, Large Language Models (LLMs) are not the off-the-shelf choice to drive multi-objective optimization yet. Conventional strategies rank high in benchmarks due to their intrinsic capabilities to handle numerical inputs and careful modelling choices that balance exploration and Pareto-front exploitation, as well as handle multiple (conflicting) objectives. In this paper, we close this gap by leveraging LLMs as surrogate models and candidate samplers inside a structured hierarchical search strategy. By adaptively partitioning the input space into disjoint hyperrectangular regions and ranking them with a composite score function, we restrict the generative process of the LLM to specific, high-potential sub-spaces, hence making the problem easier to solve as the LLM doesn't have to reason about the global structure of the problem, but only locally instead. We show that under standard regularity assumptions, our algorithm generates candidate solutions that converge to the true Pareto set in Hausdorff distance. Empirically, it consistently outperforms the global LLM-based multi-objective optimizer and is on par with standard evolutionary and Bayesian optimization algorithm on synthetic and real-world benchmarks.