The Role of Population Size in Rate of Evolution in Genetic Programming

  • Ting Hu
  • Wolfgang Banzhaf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5481)


Population size is a critical parameter that affects the performance of an Evolutionary Computation model. A variable population size scheme is considered potentially beneficial to improve the quality of solutions and to accelerate fitness progression. In this contribution, we discuss the relationship between population size and the rate of evolution in Genetic Programming. We distinguish between the rate of fitness progression and the rate of genetic substitutions, which capture two different aspects of a GP evolutionary process. We suggest a new indicator for population size adjustment during an evolutionary process by measuring the rate of genetic substitutions. This provides a separate feedback channel for evolutionary process control, derived from concepts of population genetics. We observe that such a strategy can stabilize the rate of genetic substitutions and effectively accelerate fitness progression. A test with the Mackey-Glass time series prediction verifies our observations.


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  1. 1.
    Arabas, J., Michalewicz, Z., Mulawka, J.: GAVaPS – a genetic algorithm with varying population size. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 1994), pp. 73–78. IEEE Press, Los Alamitos (1994)Google Scholar
  2. 2.
    Back, T., Eiben, A.E., van der Vaart, N.A.L.: An empirical study on GAs “without parameters”. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 315–324. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Downing, R.M.: On population size and neutrality: Facilitating the evolution of evolvability. In: Ebner, M., O’Neill, M., Ekárt, A., Vanneschi, L., Esparcia-Alcázar, A.I. (eds.) EuroGP 2007. LNCS, vol. 4445, pp. 181–192. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Eiben, A.E., Marchiori, E., Valkó, V.A.: Evolutionary algorithms with on-the-fly population size adjustment. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 41–50. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Fernandes, C., Rosa, A.: Self-regulated population size in evolutionary algorithms. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 920–929. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Fisher, R.A.: Genetical Theory of Natural Selection. Clarendon, Oxford (1930)CrossRefzbMATHGoogle Scholar
  7. 7.
    Gillespie, J.H.: The role of population size in molecular evolution. Theoretical Population Biology 55(2), 145–156 (1999)CrossRefzbMATHGoogle Scholar
  8. 8.
    Goldberg, D.E.: Sizing populations for serial and parallel genetic algorithms. In: Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 70–79. Morgan Kaufmann, San Francisco (1989)Google Scholar
  9. 9.
    Goldberg, D.E., Deb, K., Clark, J.H.: Genetic algorithms, noise, and the sizing of populations. Complex Systems 6(4), 333–362 (1992)zbMATHGoogle Scholar
  10. 10.
    Harik, G.R., Lobo, F.G.: A parameter-less genetic algorithm. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 1999), pp. 258–267. Morgan Kaufmann, San Francisco (1999)Google Scholar
  11. 11.
    Hawks, J., Wang, E.T., Cochran, G.M., Harpending, H.C., Moyzis, R.K.: Recent acceleration of human adaptive evolution. Proceedings of the National Academy of Sciences 104(52), 20753–20758 (2007)CrossRefGoogle Scholar
  12. 12.
    Hu, T., Banzhaf, W.: Nonsynonymous to synonymous substitution ratio k a/k s: Measurement for rate of evolution in evolutionary computation. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 448–457. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Lobo, F.G., Lima, C.F.: A review of adaptive population sizing schemes in genetic algorithms. In: Proceedings of the 2005 workshops on Genetic and Evolutionary Computation (GECCO 2005), pp. 228–234. ACM, New York (2005)CrossRefGoogle Scholar
  14. 14.
    Oakley, H.: Two scientific applications of genetic programming: stack filters and non-linear equation fitting to chaotic data. In: Kinnear, K.L., Kinnear Jr., K.E. (eds.) Advances in Genetic Programming, pp. 369–389. MIT Press, Cambridge (1994)Google Scholar
  15. 15.
    Ohta, T.: Population size and rate of evolution. Journal of Molecular Evolution 1(4), 305–314 (1972)CrossRefGoogle Scholar
  16. 16.
    Ohta, T.: The nearly neutral theory of molecular evolution. Annual Reviews in Ecology and Systematics 23(1), 263–286 (1992)CrossRefGoogle Scholar
  17. 17.
    Poli, R., McPhee, N.F., Vanneschi, L.: The impact of population size on code growth in GP: analysis and empirical validation. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO 2008), pp. 1275–1282. ACM, New York (2008)CrossRefGoogle Scholar
  18. 18.
    Sastry, K., O’Reilly, U.-M., Goldberg, D.E.: Population sizing for Genetic Programming based upon decision making. In: O’Reilly, U.-M., Yu, T., Riolo, R., Worzel, B. (eds.) Genetic Programming Theory and Practice II, pp. 49–66. Kluwer Academic Publishers, Dordrecht (2004)Google Scholar
  19. 19.
    Tomassini, M., Vanneschi, L., Cuendet, J.: A new technique for dynamic size populations in genetic programming. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2004), pp. 486–493. IEEE Press, Los Alamitos (2004)Google Scholar
  20. 20.
    Wedge, D.C., Kell, D.B.: Rapid prediction of optimum population size in genetic programming using a novel genotype - fitness correlation. In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO 2008), pp. 1315–1322. ACM, New York (2008)CrossRefGoogle Scholar
  21. 21.
    Woolfit, M., Bromham, L.: Population size and molecular evolution on islands. Proceedings of The Royal Society B 272(1578), 2277–2282 (2005)CrossRefGoogle Scholar
  22. 22.
    Working Group on Data Modeling Benchmarks. Created on July 20, 2002,
  23. 23.
    Yang, Z., Bielawski, J.P.: Statistical methods for detecting molecular adaptation. Trends in Ecology and Evolution 15(12), 496–503 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ting Hu
    • 1
  • Wolfgang Banzhaf
    • 1
  1. 1.Department of Computer ScienceMemorial UniversitySt. John’sCanada

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