Abstract
Drift towards growing size of genotypes is one outstanding and constantly disputed invariant in an overwhelming number of applications of evolutionary algorithms with variable-size structures. In contrast to previous work to reveal its fundamentals, we probabilistically analyze genotype growth by building on the idea of a “representation-less” model by Banzhaf and Langdon. Our model, called the fitness-size model, corresponds to a simple evolutionary algorithm using overproduction selection and mutation working on abstract objects retaining only fitness and size information.
The probalistic analysis offer some surprises counterr to present credence. The analysis predicts that average effective and noneffective lengths (and thus overall size) tend to be invariant over time. The same is true for the variance of the effective length. In contrast, the variance of the noneffective size features increases linearly in time, and its variation shows the trademark of a difussion process.Drift to increasing size manifest s if search biases favor boundary conditions. We present experimental results with both the implementation of the theoretical model and a standard genetic programming algorithm. Statistical results with the two implementations are similar and fit the theoretical predictions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bäck, T. and Schwefel, H. -P. (1993). An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation 1(1): 1–23.
Banzhaf, W., Nordin, P., Keller, R. and Francone, F. (1998). Genetic Programming - An Introduction. Morgan Kaufmann, San Francisco, CA.
Banzhaf, W. and Langdon, W. B. (2002). Some considerations on the reason for bloat. Genetic Programming and Evolvable Machines 3(1): 81–91.
Berg, H. C. (1993). Random walks in Biology. Princeton University Press.
Blickle, T. and Thiele, L. (1994). Genetic programming and redundancy. In Genetic Algorithms within the Framework of Evolutionary Computation (Workshop at KI-94, Saarbrücken), Hopf, J. (Ed. ), pp. 33–38, Im Stadtwald, Building 44, D-66123 Saarbrücken, Germany. Max-Planck- Institut für Informatik (MPI-I-94–241).
Gordon, D. F. and DesJardins, M. (1995). Evaluation and selection of biases in machine learning. Machine Learning 20: 5–22.
Holland, J. H. (1992). Adaptation in Natural and Artificial Systems, second edition. The MIT Press, Cambridge, MA.
Koza, John (1992). Genetic Programming: On the Programming of Computers by Natural Selection. MIT Press, Cambridge, MA, USA.
Langdon, W. B. (2000). Quadratic bloat in genetic programming. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2000), Whitley, D. et al. (Eds. ), pp. 451–458, Las Vegas, Nevada, USA. Morgan Kaufmann.
Langdon, W. B. and Poli, R. (1997). Fitness causes bloat. In Second On-line World Conference on Soft Computing in Engineering Design and Manufacturing.
Langdon, W. B. and Poli, R. (1998b). Fitness causes bloat: Mutation. In Proceedings of the First European Genetic Programming Conference (Euro GP 98), Lecture Notes in Computer Science (LNCS), Volume 1391, Banzhaf, W. et al. (Eds. ). Springer.
Luke, S. (2000a). Issues in Scaling Genetic Programming: Breeding Strategies, Tree Generation, and Code Bloat. PhD thesis, Department of Computer Science, University of Maryland, A. V. Williams Building, University of Maryland, College Park, MD 20742 USA.
Nordin, P., Francone, F. and Banzhaf, W. (1995). Explicitly defined introns and destructive crossover in genetic programming. In Proceeedings of the Workshop on Genetic Program-ming: From Theory to Real-World Applications (NRL TR 95. 2, University of Rochester), Rosca, J. P. (Ed. ), pp. 6–22.
Rosca, J. P. (1997a). Hierarchical Learning with Procedural Abstraction Mechanisms. PhD thesis, University of Rochester, Rochester, NY 14627.
Rosea, J. (1999). Characteristics and biases of evolution in genetic programming. GECCO tutorial http://www.cs.rochester.edu/u/rosca/.
Rosea, J. P. and Ballard, D. H. (1996a). Complexity drift in evolutionary computation with tree representations. Technical Report NRL5, University of Rochester, Computer Science Department, Rochester, NY, USA.
Rosea, J. P. and Ballard, D. H. (1999). Rooted-tree schemata in genetic programming. In Advances in Genetic Programming 3, L. Spector et al. (Eds. ), pp 243–271. MIT Press, Cambridge, MA, USA.
Soule, T. and Heckendorn, R. B. (2002). An analysis of the causes of code growth in genetic programming. Genetic Programming and Evolvable Machines 3(3): 283–309.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rosca, J. (2003). A Probabilistic Model of Size Drift. In: Riolo, R., Worzel, B. (eds) Genetic Programming Theory and Practice. Genetic Programming Series, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-8983-3_8
Download citation
DOI: https://doi.org/10.1007/978-1-4419-8983-3_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-4747-7
Online ISBN: 978-1-4419-8983-3
eBook Packages: Springer Book Archive