Article

A Schema Theory Analysis of the Evolution of Size in Genetic Programming with Linear Representations

Authors:

Nicholas Freitag McPhee,

Riccardo PoliAuthors Info & Claims

EuroGP '01: Proceedings of the 4th European Conference on Genetic Programming

Pages 108 - 125

Published: 18 April 2001 Publication History

Abstract

In this paper we use the schema theory presented in [20] to better understand the changes in size distribution when using GP with standard crossover and linear structures. Applications of the theory to problems both with and without fitness suggest that standard crossover induces specific biases in the distributions of sizes, with a strong tendency to over sample small structures, and indicate the existence of strong redistribution effects that may be a major force in the early stages of a GP run. We also present two important theoretical results: An exact theory of bloat, and a general theory of how average size changes on flat landscapes with glitches. The latter implies the surprising result that a single program glitch in an otherwise flat fitness landscape is sufficient to drive the average program size of an infinite population, which may have important implications for the control of code growth.

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Cited By

Silva SDignum SVanneschi L(2012)Operator equalisation for bloat free genetic programming and a survey of bloat control methodsGenetic Programming and Evolvable Machines10.1007/s10710-011-9150-513:2(197-238)Online publication date: 1-Jun-2012
https://dl.acm.org/doi/10.1007/s10710-011-9150-5
Silva SCosta E(2009)Dynamic limits for bloat control in genetic programming and a review of past and current bloat theoriesGenetic Programming and Evolvable Machines10.1007/s10710-008-9075-910:2(141-179)Online publication date: 1-Jun-2009
https://dl.acm.org/doi/10.1007/s10710-008-9075-9
Poli RMcPhee NVanneschi LRyan C(2008)The impact of population size on code growth in GPProceedings of the 10th annual conference on Genetic and evolutionary computation10.1145/1389095.1389341(1275-1282)Online publication date: 13-Jul-2008
https://dl.acm.org/doi/10.1145/1389095.1389341
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cover image Guide Proceedings

EuroGP '01: Proceedings of the 4th European Conference on Genetic Programming

April 2001

379 pages

ISBN:3540418997

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 18 April 2001

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Cited By

Silva SDignum SVanneschi L(2012)Operator equalisation for bloat free genetic programming and a survey of bloat control methodsGenetic Programming and Evolvable Machines10.1007/s10710-011-9150-513:2(197-238)Online publication date: 1-Jun-2012
https://dl.acm.org/doi/10.1007/s10710-011-9150-5
Silva SCosta E(2009)Dynamic limits for bloat control in genetic programming and a review of past and current bloat theoriesGenetic Programming and Evolvable Machines10.1007/s10710-008-9075-910:2(141-179)Online publication date: 1-Jun-2009
https://dl.acm.org/doi/10.1007/s10710-008-9075-9
Poli RMcPhee NVanneschi LRyan C(2008)The impact of population size on code growth in GPProceedings of the 10th annual conference on Genetic and evolutionary computation10.1145/1389095.1389341(1275-1282)Online publication date: 13-Jul-2008
https://dl.acm.org/doi/10.1145/1389095.1389341
Keijzer MFoster J(2007)Crossover bias in genetic programmingProceedings of the 10th European conference on Genetic programming10.5555/1763756.1763761(33-44)Online publication date: 11-Apr-2007
https://dl.acm.org/doi/10.5555/1763756.1763761
Poli RStephens C(2007)Understanding the Biases of Generalised RecombinationEvolutionary Computation10.1162/evco.2007.15.1.9515:1(95-131)Online publication date: 1-Mar-2007
https://dl.acm.org/doi/10.1162/evco.2007.15.1.95
Stringer HWu AO'Reilly U(2005)Behavior of finite population variable length genetic algorithms under random selectionProceedings of the 7th annual conference on Genetic and evolutionary computation10.1145/1068009.1068213(1249-1255)Online publication date: 25-Jun-2005
https://dl.acm.org/doi/10.1145/1068009.1068213
Poli RMcPhee NRowe J(2004)Exact Schema Theory and Markov Chain Models for Genetic Programming and Variable-length Genetic Algorithms with Homologous CrossoverGenetic Programming and Evolvable Machines10.1023/B:GENP.0000017010.41337.a75:1(31-70)Online publication date: 1-Mar-2004
https://dl.acm.org/doi/10.1023/B%3AGENP.0000017010.41337.a7
Poli R(2003)A simple but theoretically-motivated method to control bloat in genetic programmingProceedings of the 6th European conference on Genetic programming10.5555/1762668.1762688(204-217)Online publication date: 14-Apr-2003
https://dl.acm.org/doi/10.5555/1762668.1762688
Poli RMcPhee N(2003)General schema theory for genetic programming with subtree-swapping crossover: Part IIEvolutionary Computation10.1162/10636560376664682511:2(169-206)Online publication date: 1-May-2003
https://dl.acm.org/doi/10.1162/106365603766646825
Poli R(2001)Exact Schema Theory for Genetic Programming and Variable-Length Genetic Algorithms with One-Point CrossoverGenetic Programming and Evolvable Machines10.1023/A:10115523138212:2(123-163)Online publication date: 1-Jun-2001
https://dl.acm.org/doi/10.1023/A%3A1011552313821

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