Abstract
This chapter derives a population sizing relationship for genetic programming (GP). Following the population-sizing derivation for genetic algorithms in (Goldberg et al., 1992), it considers building block decision-making as a key facet. The analysis yields a GP-unique relationship because it has to account for bloat and for the fact that GP solutions often use subsolutions multiple times. The population-sizing relationship depends upon tree size, solution complexity, problem difficulty and building block expression probability. The relationship is used to analyze and empirically investigate population sizing for three model GP problems named ORDER, ON-OFF and LOUD. These problems exhibit bloat to differing extents and differ in whether their solutions require the use of a building block multiple times.
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References
Cantú-Paz, E. (2000). Efficient and accurate parallel genetic algorithms. Kluwer Academic Pub, Boston, MA.
Cantú-Paz, Erick, Foster, James A., Deb, Kalyanmoy, Davis, Lawrence, Roy, Rajkumar, O’Reilly, Una-May, Beyer, Hans-Georg, Standish, Russell K., Kendall, Graham, Wilson, Stewart W., Harman, Mark, Wegener, Joachim, Dasgupta, Dipankar, Potter, Mitchell A., Schultz, Alan C, Dowsland, Kathryn A., Jonoska, Natasa, and Miller, Julian R, editors (2003). Genetic and Evolutionary Computation — GECCO 2003, Part II, volume 2724 of Lecture Notes in Computer Science. Springer.
De Jong, K. A. (1975). An analysis of the behavior of a class of genetic adaptive systems. PhD thesis, University of Michigan, Ann-Arbor, MI. (University Microfilms No. 76-9381).
Feller, W. (1970). An Introduction to Probability Theory and its Applications. Wiley, New York, NY.
Goldberg, D. E. (2002). The Design of Innovation: Lessons from and for Competent Genetic Algorithms. Kluwer Academic Publishers, Boston, Mass.
Goldberg, D. E., Deb, K., and Clark, J. H. (1992). Genetic algorithms, noise, and the sizing of populations. Complex Systems, 6(4):333–362.
Goldberg, D. E. and Rudnick, M. (1991). Genetic algorithms and the variance of fitness. Complex Systems, 5(3):265–278.
Goldberg, David E. and O’Reilly, Una-May (1998). Where does the good stuff go, and why? how contextual semantics influence program structure in simple genetic programming. In Banzhaf, Wolfgang, Poli, Riccardo, Schoenauer, Marc, and Fogarty, Terence C., editors, Proceedings of the First European Workshop on Genetic Programming, volume 1391 of LNCS, pages 16–36, Paris. Springer-Verlag.
Harik, G., Cantu-Paz, E., Goldberg, D. E., and Miller, B. L. (1999). The gambler’s ruin problem, genetic algorithms, and the sizing of populations. Evolutionary Computation, 7(3):231–253.
Holland, J. H. (1973). Genetic algorithms and the optimal allocation of trials. SI AM Journal on Computing, 2(2):88–105.
Keijzer, Maarten, O’Reilly, Una-May, Lucas, Simon M., Costa, Ernesto, and Soule, Terence, editors (2004). Genetic Programming 7th European Conference, EuroGP 2004, Proceedings, volume 3003 of LNCS, Coimbra, Portugal. Springer-Verlag.
Langdon, W. B. and Poli, Riccardo (2002). Foundations of Genetic Programming. Springer-Verlag.
Luke, Sean (2000a). Code growth is not caused by introns. In Whitley, Darrell, editor, Late Breaking Papers at the 2000 Genetic and Evolutionary Computation Conference, pages 228–235, Las Vegas, Nevada, USA.
Luke, Sean (2000b). 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.
Miller, B. L. (1997). Noise, Sampling, and Efficient Genetic Algorithms. PhD thesis, University of Illinois at Urbana-Champaign, General Engineering Department, Urbana, IL.
O’Reilly, Una-May and Goldberg, David E. (1998). How fitness structure affects subsolution acquisition in genetic programming. In Koza, John R., Banzhaf, Wolfgang, Chellapilla, Kumar, Deb, Kalyanmoy, Dorigo, Marco, Fogel, David B., Garzon, Max H., Goldberg, David E., Iba, Hitoshi, and Riolo, Rick, editors, Genetic Programming 1998: Proceedings of the Third Annual Conference, pages 269–277, University of Wisconsin, Madison, Wisconsin, USA. Morgan Kaufmann.
Reed, P., Minsker, B. S., and Goldberg, D. E. (2000). Designing a competent simple genetic algorithm for search and optimization. Water Resources Research, 36(12):3757–3761.
Riolo, Rick L. and Worzel, Bill (2003). Genetic Programming Theory and Practice. Genetic Programming Series. Kluwer, Boston, MA, USA. Series Editor-John Koza.
Sastry, K. (2001). Evaluation-relaxation schemes for genetic and evolutionary algorithms. Master’s thesis, University of Illinois at Urbana-Champaign, General Engineering Department, Urbana, IL.
Sastry, K., O’Reilly, U.-M., and Goldberg, D. E. (2004). Population sizing for genetic programming based on decision making. IlliGAL Report No. 2004026, University of Illinois at Urbana Champaign, Urbana.
Sastry, Kumara, O’Reilly, Una-May, Goldberg, David E., and Hill, David (2003). Building block supply in genetic programming. In Riolo, Rick L. and Worzel, Bill, editors, Genetic Programming Theory and Practice, chapter 9, pages 137–154. Kluwer.
Soule, Terence (2003). Operator choice and the evolution of robust solutions. In Riolo, Rick L. and Worzel, Bill, editors, Genetic Programming Theory and Practise, chapter 16, pages 257–270. Kluwer.
Soule, Terence and Heckendorn, Robert B. (2002). An analysis of the causes of code growth in genetic programming. Genetic Programming and Evolvable Machines, 3(3):283–309.
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Sastry, K., O’Reilly, UM., Goldberg, D.E. (2005). Population Sizing for Genetic Programming Based on Decision-Making. In: O’Reilly, UM., Yu, T., Riolo, R., Worzel, B. (eds) Genetic Programming Theory and Practice II. Genetic Programming, vol 8. Springer, Boston, MA. https://doi.org/10.1007/0-387-23254-0_4
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DOI: https://doi.org/10.1007/0-387-23254-0_4
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