Genetic Programming and Evolvable Machines

, Volume 8, Issue 3, pp 221–237 | Cite as

A note on the variance of rank-based selection strategies for genetic algorithms and genetic programming

  • Artem Sokolov
  • Darrell Whitley
  • Andre’ da Motta Salles Barreto
Original Paper


This paper evaluates different forms of rank-based selection that are used with genetic algorithms and genetic programming. Many types of rank based selection have exactly the same expected value in terms of the sampling rate allocated to each member of the population. However, the variance associated with that sampling rate can vary depending on how selection is implemented. We examine two forms of tournament selection and compare these to linear rank-based selection using an explicit formula. Because selective pressure has a direct impact on population diversity, we also examine the interaction between selective pressure and different mutation strategies.


Tournament selection Rank based selection Genetic algorithms Genetic programming Selective pressure 


  1. 1.
    Anderson, C.W.: Learning and Problem Solving with Multilayer Connectionist Systems. PhD thesis, Computer and Information Science, University of Massachusetts (1986)Google Scholar
  2. 2.
    Blickle, T., Thiele, L.: A comparison of selection schemes used in genetic algorithms. Technical Report 11, Swiss Federal Institute of Technology (ETH), Computer Engineering and Communication Networks Lab, Zurich, Switzerland, December (1995)Google Scholar
  3. 3.
    Blickle, T., Thiele, L.: A comparison of selection schemes used in evolutionary algorithms. Evolutionary Computation, 4(4), 361–394, (1997)Google Scholar
  4. 4.
    Fogel, D.B.: Evolving Artificial Intelligence. PhD thesis, University of California, San Diego, San Diego, CA (1992)Google Scholar
  5. 5.
    Goldberg, D., Deb, K.: A comparative analysis of selection schemes used in genetic algorithms. In: G.J.E. Rawlins (ed.) Foundations of Genetic Algorithms, pp. 69–93. San Mateo, California (1991) Morgan KaufmannGoogle Scholar
  6. 6.
    Julstrom, B.A., Raidl, G.R. Weight-biased edge-crossover in evolutionary algorithms for two graph problems. In Proceedings of the 2001 ACM Symposium on Applied Computing, pp. 321–326 (2001)Google Scholar
  7. 7.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press Cambridge, MA (1992)MATHGoogle Scholar
  8. 8.
    Koza John R.: Genetic programming II: automatic discovery of reusable programs. MIT Press, Cambridge, MA, USA (1994)MATHGoogle Scholar
  9. 9.
    Motoki, T.: Calculating the expected loss of diversity of selection schemes. Evol Comput 10(4), 397–422 (2002)CrossRefGoogle Scholar
  10. 10.
    Poli, R.: Tournament selection, iterated coupon-collection problem, and backward-chaining evolutionary algorithms. In Foundations of Genetic Algorithms, pp. 132–155. Springer (2005)Google Scholar
  11. 11.
    Reinelt, G.: The Traveling Salesman: Computational Solutions for TSP Applications. Springer, Berlin (1994)Google Scholar
  12. 12.
    Schwefel, H.-P.: Evolution and Optimum Seeking. Wiley, New York (1995)Google Scholar
  13. 13.
    Sokolov, A., Whitley, D.: Unbiased tournament selection. In Proceedings of the 7th Genetic and Evolutionary Computation Conference, pp. 1131–1138 (2005)Google Scholar
  14. 14.
    Suh, J.Y., Van Gucht, D.: Distributed Genetic Algorithms. Technical report, Indiana University, Bloomington, Indiana (1987)Google Scholar
  15. 15.
    Syswerda, G.: Uniform Crossover in Genetic Algorithms. In: Schaffer, J.D. (ed.) Proceedings of The Third International Conference on Genetic Algorithms. Morgan Kaufmann (1989)Google Scholar
  16. 16.
    Whitley, D.: The genitor algorithm and selection pressure: Why rank-based allocation of reproductive trials is best. In: Proceedings of The Third International Conference on Genetic Algorithms, pp. 116–121. San Mateo, California, ISA (1989) Morgan Kaufmann PublishersGoogle Scholar
  17. 17.
    Whitley, D., Dominic, S., Das, R., Anderson, C.W.: Genetic reinforcement learning for neurocontrol problems. Mach. Learn. 13(2–3),259–284 (1993)CrossRefGoogle Scholar
  18. 18.
    Whitley, D., Kauth, J.: GENITOR: A Different Genetic Algorithm. In: Proceedings of the 1988 Rocky Mountain Conference on Artificial Intelligence (1988)Google Scholar
  19. 19.
    Whitley, D.., Rana, S., Dzubera, J., Mathias, K.E.: Evaluating evolutionary algorithms. Arti. Intelligence 85, 245–276 (1996)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Artem Sokolov
    • 1
  • Darrell Whitley
    • 1
  • Andre’ da Motta Salles Barreto
    • 2
  1. 1.Department of Computer ScienceColorado State UniversityFort CollinsUSA
  2. 2.Programa de Engenharia Civil/COPPEUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

Personalised recommendations