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*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.
@article{arxiv.2204.06461,
title = {Population Diversity Leads to Short Running Times of Lexicase Selection},
author = {Thomas Helmuth and Johannes Lengler and William La Cava},
journal= {arXiv preprint arXiv:2204.06461},
year = {2022}
}