Evolution of Iterative Formulas Using Cartesian Genetic Programming

  • Milos Minarik
  • Lukas Sekanina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6881)


Many functions such as division or square root are implemented in hardware using iterative algorithms. We propose a genetic programming-based method to automatically design simple iterative algorithms from elementary functions. In particular, we demonstrated that Cartesian Genetic Programming can evolve various iterative formulas for tasks such as division or determining the greatest common divisor using a reasonable computational effort.


Genetic Program Iterative Algorithm Crossover Probability Great Common Divisor Euclidean Algorithm 
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.


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  1. 1.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  2. 2.
    Koza, J.R.: Genetic Programming II: Automatic Discovery of Reusable Programs. MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  3. 3.
    Koza, J.R.: Human-competitive results produced by genetic programming. Genetic Programming and Evolvable Machines 11, 251–284 (2010)CrossRefGoogle Scholar
  4. 4.
    Schmidt, M.D., Lipson, H.: Coevolution of Fitness Predictors. IEEE Transactions on Evolutionary Computation 12, 736–749 (2008)CrossRefGoogle Scholar
  5. 5.
    Harding, S., Miller, J.F., Banzhaf, W.: Developments in cartesian genetic programming: self-modifying cgp. Genetic Programming and Evolvable Machines 11, 397–439 (2010)CrossRefGoogle Scholar
  6. 6.
    Sekanina, L., Bidlo, M.: Evolutionary design of arbitrarily large sorting networks using development. Genetic Programming and Evolvable Machines 6, 319–347 (2005)CrossRefGoogle Scholar
  7. 7.
    Miller, J.F., Thomson, P.: Cartesian Genetic Programming. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 121–132. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Harding, S., Miller, J.F., Banzhaf, W.: Self modifying cartesian genetic programming: Parity. In: 2009 IEEE Congress on Evolutionary Computation, pp. 285–292. IEEE Press, Los Alamitos (2009)CrossRefGoogle Scholar
  9. 9.
    Miller, J.F., Job, D., Vassilev, V.K.: Principles in the Evolutionary Design of Digital Circuits – Part I. Genetic Programming and Evolvable Machines 1, 8–35 (2000)zbMATHGoogle Scholar
  10. 10.
    Walker, J.A., Miller, J.F.: The Automatic Acquisition, Evolution and Re-use of Modules in Cartesian Genetic Programming. IEEE Transactions on Evolutionary Computation 12, 397–417 (2008)CrossRefGoogle Scholar
  11. 11.
    Kaufmann, P., Platzner, M.: Advanced techniques for the creation and propagation of modules in cartesian genetic programming. In: Proc. of Genetic and Evolutionary Computation Conference, GECCO 2008, pp. 1219–1226. ACM, New York (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Milos Minarik
    • 1
  • Lukas Sekanina
    • 1
  1. 1.Faculty of Information TechnologyBrno University of TechnologyBrnoCzech Republic

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