# Population Diversity Leads to Short Running Times of Lexicase Selection

arXiv: https://arxiv.org/abs/2204.06461 · HTML: https://mlsanity.com/paper/2204.06461/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Apr 2022.

## Built on by (most cited first, 2 of 2)

- [Probabilistic Lexicase Selection](https://mlsanity.com/paper/2305.11681/) (2023)
- [DALex: Lexicase-like Selection via Diverse Aggregation](https://mlsanity.com/paper/2401.12424/) (2024)

## Abstract (arXiv)

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.