Fitness Landscape of Large Language Model-Assisted Automated Algorithm Search

2025-04-28

AI Summary

This paper addresses the lack of systematic characterization of fitness landscapes in Large Language Model (LLM)-assisted Automated Algorithm Search (LAS). We propose a graph-based landscape representation method, covering six algorithmic tasks and six mainstream LLMs. Our empirical analysis—first of its kind—reveals that LAS landscapes exhibit high multimodality and strong task- and model-dependent structural heterogeneity: heuristic design yields dense high-performance clusters, whereas symbolic regression shows sparse, discrete optima. We further quantify how population size modulates the exploration–exploitation trade-off. The study formally establishes landscape ruggedness and intrinsic multimodality, providing both interpretable theoretical foundations and practical hyperparameter tuning guidelines for designing effective LAS strategies.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Large Multimodal Models (LMMs)
• Constraint Satisfaction and Optimization: Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Large language models for search
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Large Language Models (LLMs) have demonstrated significant potential in algorithm design. However, when integrated into search frameworks for iterative algorithm search, the underlying fitness landscape--critical for understanding search behaviou--remains underexplored. In this paper, we illustrate and analyze the fitness landscape of LLM-assisted Algorithm Search (LAS) using a graph-based approach, where nodes represent algorithms and edges denote transitions between them. We conduct extensive evaluations across six algorithm design tasks and six commonly used LLMs. Our findings reveal that LAS landscapes are highly multimodal and rugged, particularly in combinatorial optimization tasks, with distinct structural variations across tasks and LLMs. For instance, heuristic design tasks exhibit dense clusters of high-performing algorithms, while symbolic regression tasks show sparse, scattered distributions. Additionally, we demonstrate how population size influences exploration-exploitation trade-offs and the evolving trajectory of elite algorithms. These insights not only advance our understanding of LAS landscapes but also provide practical guidance for designing more effective LAS methods.

Problem

• Exploring fitness landscape of LLM-assisted algorithm search
• Analyzing structural variations across tasks and LLMs
• Investigating population size impact on exploration-exploitation trade-offs

Innovation

• Graph-based approach for LLM-assisted algorithm search
• Analysis of multimodal fitness landscapes across tasks
• Population size impact on exploration-exploitation trade-offs