How Population Diversity Influences the Efficiency of Crossover

التفاصيل البيبلوغرافية
العنوان: How Population Diversity Influences the Efficiency of Crossover
المؤلفون: Cerf, Sacha, Lengler, Johannes
سنة النشر: 2024
المجموعة: Computer Science
مصطلحات موضوعية: Computer Science - Neural and Evolutionary Computing, 68W50
الوصف: 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 $(\mu+1)$ Genetic Algorithm on LeadingOnes. We show that the naturally evolving diversity falls short of giving a substantial speed-up for any $\mu=O(\sqrt{n}/\log^2 n)$. On the other hand, we show that even for $\mu=2$, if we simply break ties in favor of diversity then this increases diversity so much that optimization is accelerated by a constant factor.
Comment: pre-print, 30 pages
نوع الوثيقة: Working Paper
URL الوصول: http://arxiv.org/abs/2404.12268
رقم الأكسشن: edsarx.2404.12268
قاعدة البيانات: arXiv