This paper analyzes the fitness landscape of algorithmic search (LAS) using a graph-based approach using large-scale language models (LLMs). Using a graph where nodes represent algorithms and edges represent transitions between algorithms, we perform extensive evaluations of six algorithm design tasks and six LLMs. Our results reveal that LAS landscapes exhibit multiple optima and a rugged structure, particularly in combinatorial optimization tasks, and that structural changes vary across tasks and LLMs. Furthermore, we employ four algorithmic similarity measures to study their correlations with algorithm performance and operator behavior. These insights deepen our understanding of LAS landscapes and offer practical insights for designing more effective LAS methods.
