On the Use of Dynamic GP Fitness Cases in Static and Dynamic Optimisation Problems

  • Edgar Galván-López
  • Lucia Vázquez-Mendoza
  • Marc Schoenauer
  • Leonardo Trujillo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10764)


In Genetic Programming (GP), the fitness of individuals is normally computed by using a set of fitness cases (FCs). Research on the use of FCs in GP has primarily focused on how to reduce the size of these sets. However, often, only a small set of FCs is available and there is no need to reduce it. In this work, we are interested in using the whole FCs set, but rather than adopting the commonly used GP approach of presenting the entire set of FCs to the system from the beginning of the search, referred as static FCs, we allow the GP system to build it by aggregation over time, named as dynamic FCs, with the hope to make the search more amenable. Moreover, there is no study on the use of FCs in Dynamic Optimisation Problems (DOPs). To this end, we also use the Kendall Tau Distance (KTD) approach, which quantifies pairwise dissimilarities among two lists of fitness values. KTD aims to capture the degree of a change in DOPs and we use this to promote structural diversity. Results on eight symbolic regression functions indicate that both approaches are highly beneficial in GP.



EGL would like to thank the TAU group at INRIA Saclay for hosting him during the outgoing phase of his Marie Curie fellowship and for financially supporting him to present this work at the conference. LT would like to thank CONACYT (project FC-2015-2:944) for providing partial funding.


  1. 1.
    Galván-López, E., Ait ElHara, O.: Using fitness comparison disagreements as a metric for promoting diversity in dynamic optimisation problems. In: IEEE Symposium Series on Computational Intelligence. Springer (2016)Google Scholar
  2. 2.
    Galván-López, E., McDermott, J., O’Neill, M., Brabazon, A.: Defining locality in genetic programming to predict performance. In: IEEE Congress on Evolutionary Computation, pp. 1–8 (2010)Google Scholar
  3. 3.
    Galván-López, E., McDermott, J., O’Neill, M., Brabazon, A.: Towards an understanding of locality in genetic programming. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, GECCO 2010, pp. 901–908. ACM, New York (2010)Google Scholar
  4. 4.
    Galván-López, E., McDermott, J., O’Neill, M., Brabazon, A.: Defining locality as a problem difficulty measure in genetic programming. Genet. Program. Evolvable Mach. 12(4), 365–401 (2011)CrossRefGoogle Scholar
  5. 5.
    Galván-López, E., Mezura-Montes, E., Ait ElHara, O., Schoenauer, M.: On the use of semantics in multi-objective genetic programming. In: Handl, J., Hart, E., Lewis, P.R., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds.) PPSN 2016. LNCS, vol. 9921, pp. 353–363. Springer, Cham (2016). CrossRefGoogle Scholar
  6. 6.
    Galván-López, E., Trujillo, L., McDermott, J., Kattan, A.: Locality in continuous fitness-valued cases and genetic programming difficulty. In: Schütze, O., Coello, C.A.C., Tantar, A., Tantar, E., Bouvry, P., Moral, P.D., Legrand, P. (eds.) EVOLVE 2012. AISC, vol. 175, pp. 41–56. Springer, Heidelberg (2012). CrossRefGoogle Scholar
  7. 7.
    Galván-López, E., Vázquez-Mendoza, L., Schoenauer, M., Trujillo, L.: Dynamic GP fitness cases in static and dynamic optimisation problems. In: Bosman, P.A.N. (ed.) Genetic and Evolutionary Computation Conference, Berlin, Germany, 15–19 July 2017, Companion Material Proceedings, pp. 227–228. ACM (2017)Google Scholar
  8. 8.
    Galván-López, E., Vázquez-Mendoza, L., Trujillo, L.: Stochastic semantic-based multi-objective genetic programming optimisation for classification of imbalanced data. In: Pichardo-Lagunas, O., Miranda-Jiménez, S. (eds.) MICAI 2016. LNCS (LNAI), vol. 10062, pp. 261–272. Springer, Cham (2017). CrossRefGoogle Scholar
  9. 9.
    Gathercole, C., Ross, P.: Dynamic training subset selection for supervised learning in genetic programming. In: Davidor, Y., Schwefel, H.-P., Männer, R. (eds.) PPSN 1994. LNCS, vol. 866, pp. 312–321. Springer, Heidelberg (1994). CrossRefGoogle Scholar
  10. 10.
    Giacobini, M., Tomassini, M., Vanneschi, L.: Limiting the number of fitness cases in genetic programming using statistics. In: Guervós, J.J.M., Adamidis, P., Beyer, H.-G., Schwefel, H.-P., Fernández-Villacañas, J.-L. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 371–380. Springer, Heidelberg (2002). Google Scholar
  11. 11.
    Gonçalves, I., Silva, S.: Balancing learning and overfitting in genetic programming with interleaved sampling of training data. In: Krawiec, K., Moraglio, A., Hu, T., Etaner-Uyar, A.Ş., Hu, B. (eds.) EuroGP 2013. LNCS, vol. 7831, pp. 73–84. Springer, Heidelberg (2013). CrossRefGoogle Scholar
  12. 12.
    Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 184–192. Morgan Kaufmann (1995)Google Scholar
  13. 13.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  14. 14.
    La Cava, W., Spector, L., Danai, K.: Epsilon-lexicase selection for regression. In: Proceedings of the Genetic and Evolutionary Computation Conference 2016, GECCO 2016, pp. 741–748. ACM, New York (2016)Google Scholar
  15. 15.
    Lasarczyk, C.W.G., Dittrich, P.W.G., Banzhaf, W.W.G.: Dynamic subset selection based on a fitness case topology. Evol. Comput. 12(2), 223–242 (2004)CrossRefGoogle Scholar
  16. 16.
    López, U., Trujillo, L., Martinez, Y., Legrand, P., Naredo, E., Silva, S.: RANSAC-GP: dealing with outliers in symbolic regression with genetic programming. In: McDermott, J., Castelli, M., Sekanina, L., Haasdijk, E., García-Sánchez, P. (eds.) EuroGP 2017. LNCS, vol. 10196, pp. 114–130. Springer, Cham (2017). CrossRefGoogle Scholar
  17. 17.
    Macedo, J., Costa, E., Marques, L.: Genetic programming algorithms for dynamic environments. In: Squillero, G., Burelli, P. (eds.) EvoApplications 2016. LNCS, vol. 9598, pp. 280–295. Springer, Cham (2016). CrossRefGoogle Scholar
  18. 18.
    Martínez, Y., Naredo, E., Trujillo, L., Legrand, P., López, U.: A comparison of fitness-case sampling methods for genetic programming. J. Exp. Theor. Artif. Intell. 1–22 (2017)Google Scholar
  19. 19.
    McDermott, J., et al.: Genetic programming needs better benchmarks. In: Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation, GECCO 2012, pp. 791–798. ACM, New York (2012)Google Scholar
  20. 20.
    Nguyen, T.T., Yang, S., Branke, J.: Evolutionary dynamic optimization: a survey of the state of the art. Swarm Evol. Comput. 6, 1–24 (2012)CrossRefGoogle Scholar
  21. 21.
    Riekert, M., Malan, K.M., Engelbrect, A.P.: Adaptive genetic programming for dynamic classification problems. In: Proceedings of the Eleventh Conference on Congress on Evolutionary Computation, CEC 2009, pp. 674–681. IEEE Press, Piscataway (2009)Google Scholar
  22. 22.
    Spector, L.: Assessment of problem modality by differential performance of lexicase selection in genetic programming: a preliminary report. In: Proceedings of the Fourteenth International Conference on Genetic and Evolutionary Computation Conference Companion, GECCO Companion 2012, pp. 401–408. ACM (2012)Google Scholar
  23. 23.
    Teller, A., Andre, D.: Automatically choosing the number of fitness cases: the rational allocation of trials. In: Koza, J.R., et al. (eds.) Genetic Programming 1997: Proceedings of the Second Annual Conference, Stanford University, CA, USA, 13–16 July 1997, pp. 321–328. Morgan Kaufmann (1997)Google Scholar
  24. 24.
    Vanneschi, L., Cuccu, G.: A study of genetic programming variable population size for dynamic optimization problems. In: IJCCI, pp. 119–126 (2009)Google Scholar
  25. 25.
    Wagner, N., Michalewicz, Z., Khouja, M., McGregor, R.R.: Time series forecasting for dynamic environments: the DyFor genetic program model. IEEE Trans. Evol. Comput. 11(4), 433–452 (2007)CrossRefGoogle Scholar
  26. 26.
    Zhang, B.-T., Cho, D.-Y.: Genetic programming with active data selection. In: McKay, B., Yao, X., Newton, C.S., Kim, J.-H., Furuhashi, T. (eds.) SEAL 1998. LNCS (LNAI), vol. 1585, pp. 146–153. Springer, Heidelberg (1999). CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Edgar Galván-López
    • 1
  • Lucia Vázquez-Mendoza
    • 2
  • Marc Schoenauer
    • 3
  • Leonardo Trujillo
    • 4
  1. 1.Department of Computer ScienceNational University of Ireland MaynoothMaynoothIreland
  2. 2.School of Social Sciences and PhilosophyTrinity College DublinDublinIreland
  3. 3.TAU, INRIA and LRI, CNRS & U. Paris-Sud, Université Paris-SaclayParisFrance
  4. 4.Posgrado en Ciencias de la IngenieríaInstituto Tecnológico de TijuanaTijuanaMexico

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