Abstract
This paper presents a simple method to control bloat which is based on the idea of strategically and dynamically creating fitness “holes” in the fitness landscape which repel the population. In particular we create holes by zeroing the fitness of a certain proportion of the offspring that have above average length. Unlike other methods where all individuals are penalised when length constraints are violated, here we randomly penalise only a fixed proportion of all the constraintviolating offspring. The paper describes the theoretical foundation for this method and reports the results of its empirical validation with two relatively hard test problems, which has confirmed the effectiveness of the approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
T. Blickle. Evolving compact solutions in genetic programming:Acase study. In H.-M. Voigt, W. Ebeling, I. Rechenberg, and H.-P. Schwefel, editors, Parallel Problem Solving From Nature IV. Proceedings of the International Conference on Evolutionary Computation, volume 1141 of LNCS, pages 564–573, Berlin, Germany, 22–26 Sept. 1996. Springer-Verlag.
T. Blickle and L. Thiele. Genetic programming and redundancy. In J. Hopf, editor, Genetic Algorithms within the Framework of Evolutionary Computation (Workshop at KI-94, Saarbrücken), pages 33–38, Im Stadtwald, Building 44, D-66123 Saarbrücken, Germany, 1994. Max-Planck-Institut für Informatik (MPI-I-94-241).
A. Ekart and S. Z. Nemeth. Selection based on the pareto nondomination criterion for controlling code growth in genetic programming. Genetic Programming and Evolvable Machines, 2(1):61–73, Mar. 2001.
C. Gathercole and P. Ross. An adverse interaction between crossover and restricted tree depth in genetic programming. In J. R. Koza, D. E. Goldberg, D. B. Fogel, and R. L. Riolo, editors, Genetic Programming 1996: Proceedings of the First Annual Conference, pages 291–296, Stanford University, CA, USA, 28–31 July 1996. MIT Press.
D. C. Hooper, N. S. Flann, and S. R. Fuller. Recombinative hill-climbing: A stronger search method for genetic programming. In J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, H. Iba, and R. L. Riolo, editors, Genetic Programming 1997: Proceedings of the Second Annual Conference, pages 174–179, Stanford University, CA, USA, 13–16 July 1997. Morgan Kaufmann.
H. Iba, H. de Garis, and T. Sato. Genetic programming using a minimum description length principle. In K. E. Kinnear, Jr., editor, Advances in Genetic Programming, chapter 12, pages 265–284. MIT Press, 1994.
J. R. Koza. A genetic approach to the truck backer upper problem and the inter-twined spiral problem. In Proceedings of IJCNN International Joint Conference on Neural Networks, volume IV, pages 310–318. IEEE Press, 1992.
J. R. Koza. Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, USA, 1992.
W. B. Langdon. Scaling of program tree fitness spaces. Evolutionary Computation, 7(4):399–428,Winter 1999.
W. B. Langdon. Size fair and homologous tree genetic programming crossovers. In W. Banzhaf, J. Daida, A. E. Eiben, M. H. Garzon, V. Honavar, M. Jakiela, and R. E. Smith, editors, Proceedings of the Genetic and Evolutionary Computation Conference, volume 2, pages 1092–1097, Orlando, Florida, USA, 13–17 July 1999. Morgan Kaufmann.
W. B. Langdon. Quadratic bloat in genetic programming. In D. Whitley, D. Goldberg, E. Cantu-Paz, L. Spector, I. Parmee, and H.-G. Beyer, editors, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2000), pages 451–458, LasVegas, Nevada, USA, 10–12 July 2000. Morgan Kaufmann.
W. B. Langdon. Size fair and homologous tree genetic programming crossovers. Genetic Programming and Evolvable Machines, 1(1/2):95–119, Apr. 2000.
W. B. Langdon and W. Banzhaf. Genetic programming bloat without semantics. In M. Schoenauer, K. Deb, G. Rudolph, X. Yao, E. Lutton, J. J. Merelo, and H.-P. Schwefel, editors, Parallel Problem Solving from Nature-PPSNVI 6th International Conference, volume 1917 of LNCS, pages 201–210, Paris, France, 16–20 Sept. 2000. Springer Verlag.
W. B. Langdon and R. Poli. An analysis of the MAX problem in genetic programming. In J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, H. Iba, and R. L. Riolo, editors, Genetic Programming 1997: Proceedings of the Second Annual Conference, pages 222–230, Stanford University, CA, USA, 13–16 July 1997. Morgan Kaufmann.
W. B. Langdon and R. Poli. Why ants are hard. In J. R. Koza, W. Banzhaf, K. Chellapilla, K. Deb, M. Dorigo, D. B. Fogel, M. H. Garzon, D. E. Goldberg, H. Iba, and R. Riolo, editors, Genetic Programming 1998: Proceedings of the Third Annual Conference, pages 193–201, University ofWisconsin, Madison,Wisconsin, USA, 22–25 July 1998. Morgan Kaufmann.
W. B. Langdon and R. Poli. Foundations of Genetic Programming. Springer-Verlag, 2002.
W. B. Langdon, T. Soule, R. Poli, and J. A. Foster. The evolution of size and shape. In L. Spector, W. B. Langdon, U.-M. O’Reilly, and P. J. Angeline, editors, Advances in Genetic Programming 3, chapter 8, pages 163–190. MIT Press, Cambridge, MA, USA, June 1999.
N. F. McPhee and J. D. Miller. Accurate replication in genetic programming. In L. Eshelman, editor, Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA95), pages 303–309, Pittsburgh, PA, USA, 15–19 July 1995. Morgan Kaufmann.
N. F. McPhee and R. Poli. A schema theory analysis of the evolution of size in genetic programming with linear representations. In Genetic Programming, Proceedings of EuroGP 2001, LNCS, Milan, 18–20 Apr. 2001. Springer-Verlag.
P. Nordin and W. Banzhaf. Complexity compression and evolution. In L. Eshelman, editor, Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA95), pages 310–317, Pittsburgh, PA, USA, 15–19 July 1995. Morgan Kaufmann.
P. Nordin, F. Francone, and W. Banzhaf. Explicitly defined introns and destructive crossover in genetic programming. In P. J. Angeline and K. E. Kinnear, Jr., editors, Advances in Genetic Programming 2, chapter 6, pages 111–134. MIT Press, Cambridge, MA, USA, 1996.
U.-M. O’Reilly and F. Oppacher. Hybridized crossover-based search techniques for program discovery. In Proceedings of the 1995 World Conference on Evolutionary Computation, volume 2, pages 573–578, Perth, Australia, 29 Nov–1 Dec. 1995. IEEE Press.
R. Poli. General schema theory for genetic programming with subtree-swapping crossover. In J. F. Miller, M. Tomassini, P. L. Lanzi, C. Ryan, A. G. B. Tettamanzi, and W. B. Langdon, editors, Genetic Programming, Proceedings of EuroGP’2001, volume 2038 of LNCS, pages 143–159, Lake Como, Italy, 18–20 Apr. 2001. Springer-Verlag.
K. Rodriguez-Vazquez, C. M. Fonseca, and P. J. Fleming. Multiobjective genetic programming: A nonlinear system identification application. In J. R. Koza, editor, Late Breaking Papers at the 1997 Genetic Programming Conference, pages 207–212, Stanford University, CA, USA, 13–16 July 1997. Stanford Bookstore.
J. P. Rosca. Analysis of complexity drift in genetic programming. In J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, H. Iba, and R. L. Riolo, editors, Genetic Programming 1997: Proceedings of the Second Annual Conference, pages 286–294, Stanford University, CA, USA, 13–16 July 1997. Morgan Kaufmann.
T. Soule. Code Growth in Genetic Programming. PhD thesis, University of Idaho, Moscow, Idaho, USA, 15 May 1998.
T. Soule and J. A. Foster. Code size and depth flows in genetic programming. In J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, H. Iba, and R. L. Riolo, editors, Genetic Programming 1997: Proceedings of the Second Annual Conference, pages 313–320, Stanford University, CA, USA, 13–16 July 1997. Morgan Kaufmann.
T. Soule and J. A. Foster. Effects of code growth and parsimony pressure on populations in genetic programming. Evolutionary Computation, 6(4):293–309,Winter 1998.
T. Soule and J. A. Foster. Removal bias: a new cause of code growth in tree based evolutionary programming. In 1998 IEEE International Conference on Evolutionary Computation, pages 781–186, Anchorage, Alaska, USA, 5–9 May 1998. IEEE Press.
T. Soule and R. B. Heckendorn. An analysis of the causes of code growth in genetic programming. Genetic Programming and Evolvable Machines, 3(3):283–309, Sept. 2002.
B.-T. Zhang and H. Mühlenbein. Balancing accuracy and parsimony in genetic programming. Evolutionary Computation, 3(1):17–38, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Poli, R. (2003). A Simple but Theoretically-Motivated Method to Control Bloat in Genetic Programming. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E., Poli, R., Costa, E. (eds) Genetic Programming. EuroGP 2003. Lecture Notes in Computer Science, vol 2610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36599-0_19
Download citation
DOI: https://doi.org/10.1007/3-540-36599-0_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00971-9
Online ISBN: 978-3-540-36599-0
eBook Packages: Springer Book Archive