Abstract
Genetic Programming uses a tree based representation to express solutions to problems. Trees are constructed from a primitive set which consists of a function set and a terminal set. An extension to GP is the ability to define modules, which are in turn tree based representations defined in terms of the primitives. The most well known of these methods is Koza’s Automatically Defined Functions. In this paper it is proved that for a given problem, the minimum number of nodes in the main tree plus the nodes in any modules is independent of the primitive set (up to an additive constant) and depends only on the function being expressed. This reduces the number of user defined parameters in the run and makes the inclusion of a hypothesis in the search space independent of the primitive set.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
P. J. Angeline and J. B. Pollack. The evolutionary induction of subroutines. In Proceedings of the Fourteenth Annual Conference of the Cognitive Science Society, Bloomington, Indiana, USA, 1992. Lawrence Erlbaum.
Wolfgang Banzhaf, Peter Nordin, Robert E. Keller, and Frank D. Francone. Genetic Programming-An Introduction; On the Automatic Evolution of Computer Programs and its Applications. Morgan Kaufmann, dpunkt.verlag, January 1998.
Thomas M. Cover and Joy A. Thomas. Elements of Information Theory. Wiley Series in Telecommunications. John Wiley & Sons, New York, NY, USA, 1991.
Lorenz Huelsbergen. Toward simulated evolution of machine language iteration. In John R. Koza, David E. Goldberg, David B. Fogel, and Rick L. Riolo, editors, Genetic Programming 1996: Proceedings of the First Annual Conference, pages 315–320, Stanford University, CA, USA, 28–31 July 1996. MIT Press.
John R. Koza. Genetic Programming: On the Programming of Computers by Means f Natural Selection. MIT Press, 1992.
John R. Koza. Genetic Programming II: Automatic Discovery of Reusable Programs. IT Press, Cambridge Massachusetts, May 1994.
John R. Koza. Evolving the architecture of a multi-part program in genetic programming using architecture-altering operations. In John Robert McDonnell, Robert G. Reynolds, and David B. Fogel, editors, Evolutionary Programming IV Proceedings of the Fourth Annual Conference on Evolutionary Programming, pages 695–717, San Diego, CA, USA, 1–3 1995. MIT Press.
W. B. Langdon and Riccardo Poli. Foundations of Genetic Programming. Springer-Verlag, 2002.
Julian F. Miller and Peter Thomson. Cartesian genetic programming. In Riccardo Poli, Wolfgang Banzhaf, William B. Langdon, Julian F. Miller, Peter Nordin, and Terence C. Fogarty, editors, Genetic Programming, Proceedings of EuroGP 2000, volume 1802 of LNCS, pages 121–132, Edinburgh, 15–16 April 2000. Springer-Verlag.
J. P. Rosca and D. H. Ballard. Learning by adapting representations in genetic programming. In Proceedings of the 1994 IEEE World Congress on Computational Intelligence, Orlando, Florida, USA, Orlando, Florida, USA, 27–29 June 1994. IEEE Press.
I. Wegener. The Complexity of Boolean Functions. Wiley Teubner, 1987.
J. R. Woodward and J. R. Neil. No free lunch, program induction and combinatorial problems. In Genetic Programming, Proceedings of EuroGP 2003, Essex, UK, 14–16 April 2003. Springer-Verlag.
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
Woodward, J.R. (2003). Modularity 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_23
Download citation
DOI: https://doi.org/10.1007/3-540-36599-0_23
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