What Makes an LLM a Good Optimizer? A Trajectory Analysis of LLM-Guided Evolutionary Search

TL;DR

This study analyzes how large language models guide evolutionary search, revealing that strong optimizers act as local refiners with incremental improvements, while weaker ones drift semantically and stagnate.

Contribution

It provides a large-scale trajectory analysis of LLM-guided optimization, uncovering behaviors that differentiate effective from ineffective models and offering insights for system design.

Findings

Strong LLM optimizers act as local refiners with incremental improvements.

Weaker optimizers exhibit semantic drift and stagnation.

Solution novelty does not predict final performance unless search remains localized.

Abstract

Recent work has demonstrated the promise of orchestrating large language models (LLMs) within evolutionary and agentic optimization systems. However, the mechanisms driving these optimization gains remain poorly understood. In this work, we present a large-scale study of LLM-guided evolutionary search, collecting optimization trajectories for 15 LLMs across 8 tasks. Although zero-shot problem-solving ability correlates with final optimization outcomes, it explains only part of the variance: models with similar initial capability often induce dramatically different search trajectories and outcomes. By analyzing these trajectories, we find that strong LLM optimizers behave as local refiners, producing frequent incremental improvements while progressively localizing the search in semantic space. Conversely, weaker optimizers exhibit large semantic drift, with sporadic breakthroughs followed by stagnation. Notably, various measures of solution novelty do not predict final performance; novelty is beneficial only when the search remains sufficiently localized around high-performing regions of the solution space. Our results highlight the importance of trajectory analysis for understanding and improving LLM-based optimization systems and provide actionable insights for their design and training.