Population Diversity Leads to Short Running Times of Lexicase Selection

Thomas Helmuth, Johannes Lengler, William G. La Cava

Abstract: In this paper we investigate why the running time of lexicase parent selection is empirically much lower than its worst-case bound of $$O(N \cdot C)$$ . We define a measure of population diversity and prove that high diversity leads to low running times $$O(N + C)$$ of lexicase selection. We then show empirically that genetic programming populations evolved under lexicase selection are diverse for several program synthesis problems, and explore the resulting differences in running time bounds.