# How Population Diversity Influences the Efficiency of Crossover

arXiv: https://arxiv.org/abs/2404.12268 · HTML: https://mlsanity.com/paper/2404.12268/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2024.

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

- [Parent Selection Mechanisms in Elitist Crossover-Based Algorithms](https://mlsanity.com/paper/2604.04083/) (2026)
- [Genetic Algorithms with Optimization Guided Operators](https://mlsanity.com/paper/2606.12279/) (2026)

## Abstract (arXiv)

Our theoretical understanding of crossover is limited by our ability to analyze how population diversity evolves. In this study, we provide one of the first rigorous analyses of population diversity and optimization time in a setting where large diversity and large population sizes are required to speed up progress. We give a formal and general criterion which amount of diversity is necessary and sufficient to speed up the (μ+1) Genetic Algorithm on LeadingOnes. We show that the naturally evolving diversity falls short of giving a substantial speed-up for any μ=O(√n/log2 n). On the other hand, we show that even for μ=2, if we simply break ties in favor of diversity then this increases diversity so much that optimization is accelerated by a constant factor.