Journal of Statistical Physics

, Volume 166, Issue 3–4, pp 1065–1077

A Model with Darwinian Dynamics on a Rugged Landscape


DOI: 10.1007/s10955-016-1637-2

Cite this article as:
Brotto, T., Bunin, G. & Kurchan, J. J Stat Phys (2017) 166: 1065. doi:10.1007/s10955-016-1637-2


We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase diagram in terms of the size of the population and the diffusion rate, with a glass phase inside which the dynamics keeps searching for better configurations, and outside which deleterious ‘mutations’ spoil the performance. The phase diagram is analogous to that of dense active matter in terms of temperature and drive.


Population dynamics Glasses Genetic algorithm Glassy landscape 

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Laboratoire de Physique Statistique, École Normale SupérieurePSL Research University, Université Paris Diderot Sorbonne Paris-Cité, Sorbonne Universités UPMC Univ Paris 06, CNRSParisFrance
  2. 2.Dipartimento di FisicaUniversità degli Studi di MilanoMilanoItaly
  3. 3.INFN, Sezione di MilanoMilanoItaly
  4. 4.Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA

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