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

2026-04-21

AI Summary

This study investigates the mechanisms underlying the varying optimization capabilities of large language models (LLMs) in guiding evolutionary search. By systematically analyzing the optimization trajectories of 15 LLMs across eight tasks—integrating large-scale semantic space modeling, zero-shot capability assessment, and novelty metrics—the work reveals that strong optimizers tend to perform local semantic refinement within high-performance regions, whereas weaker ones exhibit substantial semantic drift. The findings indicate that while initial solution quality partially predicts final performance, the locality of the search process and the capacity for sustained iterative improvement are the key determinants of optimization efficacy. This research provides the first mechanistic account of LLM-guided evolutionary search, establishing a theoretical foundation for understanding how LLMs drive optimization behavior.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• LLM-guided optimization
• evolutionary search
• optimization trajectory
• semantic drift
• local refinement

Innovation

• trajectory analysis
• LLM-guided optimization
• evolutionary search
• semantic localization
• local refiner