Self modifying cartesian genetic programming: finding algorithms that calculate pi and e to arbitrary precision

Authors:
Simon Harding;Julian F. Miller;Wolfgang Banzhaf
Affiliations:
Memorial University, St John's, NF, Canada;University of York, York, United Kingdom;Memorial University, St Johns, NF, Canada
Venue:
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Year:
2010

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Abstract

Self Modifying Cartesian Genetic Programming (SMCGP) aims to be a general purpose form of developmental genetic programming. The evolved programs are iterated thus allowing an infinite sequence of phenotypes (programs) to be obtained from a single evolved genotype. In previous work this approach has already shown that it is possible to obtain mathematically provable general solutions to certain problems. We extend this class in this paper by showing how SMCGP can be used to find algorithms that converge to mathematical constants (pi and e). Mathematical proofs are given that show that some evolved formulae converge to pi and e in the limit as the number of iterations increase.