Population Diversity Leads to Short Running Times of Lexicase Selection

TL;DR

This paper demonstrates that high population diversity in lexicase selection significantly reduces its running time from worst-case bounds to near-linear, supported by theoretical proofs and empirical evidence in genetic programming.

Contribution

It introduces a population diversity measure and proves that high diversity leads to lower lexicase selection running times, supported by empirical validation.

Findings

High diversity correlates with shorter running times.

Genetic programming populations under lexicase are typically diverse.

Empirical results support the theoretical bounds.

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*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.