2024/04/18 by Sacha Cerf, Johannes Lengler, Cerf, Sacha +1 · 1 citation
Economics, Econometrics and Finance · #68W50 #FOS: Computer and information sciences #Merger and Competition Analysis #Neural and Evolutionary Computing (cs.NE)
paper · pdf · doi:10.48550/arxiv.2404.12268
openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.