What Makes an LLM a Good Optimizer? A Trajectory Analysis of LLM-Guided Evolutionary Search
Xinhao Zhang, Xi Chen, François Portet, Maxime Peyrard
TLDR
This paper analyzes LLM-guided evolutionary search trajectories to understand what makes LLMs good optimizers, finding strong models act as local refiners.
Key contributions
- Conducted a large-scale study of 15 LLMs across 8 tasks in evolutionary search.
- Identified strong LLM optimizers as local refiners, making frequent, incremental improvements.
- Observed weaker optimizers exhibit large semantic drift and sporadic breakthroughs followed by stagnation.
- Determined solution novelty is only beneficial when search remains localized in high-performing regions.
Why it matters
This work provides crucial insights into the mechanisms behind LLM-guided optimization, moving beyond simple performance metrics. Understanding search trajectories helps design more effective LLM optimizers by focusing on local refinement and controlled novelty. These findings are vital for advancing LLM-based agentic systems.
Original 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.
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