Nonsynonymous to Synonymous Substitution Ratio \(k_{\mathrm a}/k_{\mathrm s}\): Measurement for Rate of Evolution in Evolutionary Computation

  • Ting Hu
  • Wolfgang Banzhaf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


Measuring fitness progression using numeric quantification in an Evolutionary Computation (EC) system may not be sufficient to capture the rate of evolution precisely. In this paper, we define the rate of evolution \(R_{\mathrm e}\) in an EC system based on the rate of efficient genetic variations being accepted by the EC population. This definition is motivated by the measurement of “amino acid to synonymous substitution ratio” \(k_{\mathrm a}/k_{\mathrm s}\) in biology, which has been widely accepted to measure the rate of gene sequence evolution. Experimental applications to investigate the effects of four major configuration parameters on our rate of evolution measurement show that \(R_{\mathrm e}\) well reflects how evolution proceeds underneath fitness development and provides some insights into the effectiveness of EC parameters in evolution acceleration.


Evolutionary Computation Synonymous Substitution Average Fitness Crossover Rate Nonsynonymous Substitution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Banzhaf, W., Beslon, G., Christensen, S., Foster, J.A., Kepes, F., Lefort, V., Miller, J.F., Radman, M., Ramsden, J.J.: From artificial evolution to computational evolution: A research agenda. Nature Reviews Genetics 7(9), 729–735 (2006)CrossRefGoogle Scholar
  2. 2.
    Banzhaf, W., Nordin, P., Keller, R.E., Francone, F.D.: Genetic Programming: An Introduction On the Automatic Evolution of Computer Programs and Its Applications. Morgan Kaufmann Publishers, San Francisco (1998)CrossRefzbMATHGoogle Scholar
  3. 3.
    Bedau, M.A., Packard, N.H.: Measurement of evolutionary activity, teleology, and life. In: Artificial Life II, pp. 431–461. Addison-Wesley, Redwood City (1992)Google Scholar
  4. 4.
    Hu, T., Banzhaf, W.: Measuring rate of evolution in genetic programming using amino acid to synonymous substitution ratio \(k_{\mathrm a}/k_{\mathrm s}\). In: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation (GECCO 2008), Atlanta, GA, pp. 1337–1338 (2008)Google Scholar
  5. 5.
    Koza, J.R.: Genetic programming II: automatic discovery of reusable programs. MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  6. 6.
    Langdon, W.B., Banzhaf, W.: Repeated patterns in tree genetic programming. In: Proceedings of the 8th European Conference on Genetic Programming, Lausanne, Switzerland, pp. 190–202 (2005)Google Scholar
  7. 7.
    Luke, S., Panait, L.: A Comparison of Bloat Control Methods for Genetic Programming. Evolutionary Computation 14(3), 309–334 (2006)CrossRefGoogle Scholar
  8. 8.
    Miyata, T., Yasunaga, T.: Molecular evolution of mRNA: A method for estimating evolutionary rates of synonymous and amino acid substitutions from homologous nucleotide sequences and its application. Journal of Molecular Evolution 16(1), 23–36 (1980)CrossRefGoogle Scholar
  9. 9.
    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 2008

Authors and Affiliations

  • Ting Hu
    • 1
  • Wolfgang Banzhaf
    • 1
  1. 1.Department of Computer ScienceMemorial University of NewfoundlandCanada

Personalised recommendations