Reconstructing Dynamic Target Functions by Means of Genetic Programming Using Variable Population Size

  • Leonardo Vanneschi
  • Giuseppe Cuccu
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 343)


Dynamic environments are becoming more and more popular in many applicative domains. A large amount of literature has appeared to date dealing with the problem of tracking the extrema of dynamically changing target functions, but relatively few material has been produced on the problem of reconstructing the shape, or more generally finding the equation, of dynamically changing target functions. Nevertheless, in many applicative domains, reaching this goal would have an extremely important impact. It is the case, for instance, of complex systems modelling, like for instance biological systems or systems of biochemical reactions, where one is generally interested in understanding what’s going on in the system over time, rather than following the extrema of some target functions. Last but not least, we also believe that being able to reach this goal would help researchers to have a useful insight on the reasons that cause the change in the system over time, or at least the pattern of this modification. This paper is intended as a first preliminary step in the attempt to fill this gap. We show that genetic programming with variable population size is able to adapt to the environment modifications much faster (i.e. using a noteworthy smaller amount of computational effort) than standard genetic programming using fixed population size. The suitability of this model is tested on a set of benchmarks based on some well known symbolic regression problems.


Particle Swarm Optimization Genetic Programming Target Function Dynamic Optimization Dynamic Optimization Problem 
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.
    Banzhaf, W., Langdon, W.B.: Some considerations on the reason of bloat. Genetic Programming and Evolvable Machines 3, 81–91 (2002)CrossRefzbMATHGoogle Scholar
  2. 2.
    Branke, J.: Memory enhanced evolutionary algorithms for changing optimization problems. In: Congress on Evolutionary Computation CEC 1999, vol. 3, pp. 1875–1882. IEEE, Los Alamitos (1999)Google Scholar
  3. 3.
    Branke, J.: Evolutionary approaches to dynamic environments - updated survey. In: GECCO Workshop on Evolutionary Algorithms for Dynamic Optimization Problems, pp. 27–30 (2001)Google Scholar
  4. 4.
    Branke, J.: Evolutionary Optimization in Dynamic Environments. Kluwer, Dordrecht (2001)Google Scholar
  5. 5.
    Branke, J.: Evolutionary approaches to dynamic optimization problems – introduction and recent trends. In: Branke, J. (ed.) GECCO Workshop on Evolutionary Algorithms for Dynamic Optimization Problems, pp. 2–4 (2003)Google Scholar
  6. 6.
    Branke, J., Kauler, T., Schmidt, C., Schmeck, H.: A multi-population approach to dynamic optimization problems. In: Adaptive Computing in Design and Manufacturing, pp. 299–308. Springer, Heidelberg (2000)Google Scholar
  7. 7.
    Burke, E., Gustafson, S., Kendall, G., Krasnogor, N.: Advanced population diversity measures in genetic programming. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 341–350. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Clerc, M.: Particle Swarm Optimization. ISTE (2006)Google Scholar
  9. 9.
    Cobb, H.G.: An investigation into the use of hypermutation as an adaptive operator in genetic algorithms having continuous, time-dependent nonstationary environments. Technical Report ADA229159, Naval Research Lab, Washington DC (1990)Google Scholar
  10. 10.
    Dasgupta, D., Mcgregor, D.R.: Nonstationary function optimization using the structured genetic algorithm. In: Parallel Problem Solving From Nature, pp. 145–154. Elsevier, Amsterdam (1992)Google Scholar
  11. 11.
    de França, F.O., Von Zuben, F.J., de Castro, L.N.: An artificial immune network for multimodal function optimization on dynamic environments. In: GECCO 2005: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 289–296. ACM, New York (2005)CrossRefGoogle Scholar
  12. 12.
    Dempsey, I.: Grammatical Evolution in Dynamic Environments. PhD thesis, University College Dublin, Ireland (2007)Google Scholar
  13. 13.
    Fernandes, C., Ramos, V., Rosa, A.C.: Varying the population size of artificial foraging swarms on time varying landscapes. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3696, pp. 311–316. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Fernández, F., Tomassini, M., Vanneschi, L.: An empirical study of multipopulation genetic programming. Genetic Programming and Evolvable Machines 4(1), 21–52 (2003)CrossRefzbMATHGoogle Scholar
  15. 15.
    Fernández, F., Tomassini, M., Vanneschi, L.: Saving computational effort in genetic programming by means of plagues. In: Congress on Evolutionary Computation (CEC 2003), Canberra, Australia, pp. 2042–2049. IEEE Press, Piscataway (2003)CrossRefGoogle Scholar
  16. 16.
    Fernández, F., Vanneschi, L., Tomassini, M.: The effect of plagues in genetic programming: A study of variable size populations. In: Ryan, C., et al. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 317–326. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. 17.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)zbMATHGoogle Scholar
  18. 18.
    Goldberg, D.E., Smith, R.E.: Nonstationary function optimization using genetic algorithms with dominance and diploidy. In: ICGA, pp. 59–68 (1987)Google Scholar
  19. 19.
    Grefenstette, J.J.: Genetic algorithms for changing environments. In: Parallel Problem Solving from Nature, vol. 2, pp. 137–144 (1992)Google Scholar
  20. 20.
    Huang, C.-F., Rocha, L.M.: Tracking extrema in dynamic environments using a coevolutionary agent-based model of genotype edition. In: GECCO 2005: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 545–552. ACM, New York (2005)CrossRefGoogle Scholar
  21. 21.
    Keijzer, M.: Improving symbolic regression with interval arithmetic and linear scaling. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 71–83. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  22. 22.
    Koza, J.R.: Genetic Programming. The MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  23. 23.
    Mori, N., Kita, H., Nishikawa, Y.: Adaptation to a changing environment by means of the feedback thermodynamical genetic algorithm. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 513–522. Springer, Heidelberg (1998)Google Scholar
  24. 24.
    Ng, K.P., Wong, K.C.: A new diploid scheme and dominance change mechanism for non-stationary function optimization. In: Proceedings of the 6th International Conference on Genetic Algorithms, pp. 159–166. Morgan Kaufmann Publishers Inc., San Francisco (1995)Google Scholar
  25. 25.
    Poli, R., Langdon, W.B., McPhee, N.F.: A field guide to genetic programming (2008), Published via,, (With contributions by J. R. Koza)
  26. 26.
    Rand, W., Riolo, R.: The problem with a self-adaptative mutation rate in some environments: a case study using the shaky ladder hyperplane-defined functions. In: GECCO 2005: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 1493–1500. ACM, New York (2005)CrossRefGoogle Scholar
  27. 27.
    Tanev, I.: Genetic programming incorporating biased mutation for evolution and adaptation of snakebot. Genetic Programming and Evolvable Machines 8(1), 39–59 (2007)CrossRefGoogle Scholar
  28. 28.
    Tomassini, M., Vanneschi, L., Cuendet, J., Fernández, F.: A new technique for dynamic size populations in genetic programming. In: Proceedings of the 2004 IEEE Congress on Evolutionary Computation (CEC 2004), Portland, Oregon, USA, pp. 486–493. IEEE Press, Piscataway (2004)CrossRefGoogle Scholar
  29. 29.
    Tsutsui, S., Fujimoto, Y., Ghosh, A.: Forking genetic algorithms: Gas with search space division schemes. Evol. Comput. 5(1), 61–80 (1997)CrossRefGoogle Scholar
  30. 30.
    Vavak, F., Jukes, K., Fogarty, T.C.: Learning the local search range for genetic optimisation in nonstationary environments. In: IEEE Intl. Conf. on Evolutionary Computation ICEC 1997, pp. 355–360. IEEE Publishing, Los Alamitos (1997)CrossRefGoogle Scholar
  31. 31.
    Yang, S.: Constructing dynamic test environments for genetic algorithms based on problem difficulty. In: Congress on Evolutionary Computation, CEC 2004, vol. 2, pp. 1262–1269. IEEE, Piscataway (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Leonardo Vanneschi
    • 1
  • Giuseppe Cuccu
    • 2
  1. 1.Dipartimento di Informatica, Sistemistica e Comunicazione (D.I.S.Co.)University of Milano-BicoccaMilanItaly
  2. 2.Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA)LuganoSwitzerland

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