Genetic programming for finite algebras

Authors:
Lee Spector;David M. Clark;Ian Lindsay;Bradford Barr;Jon Klein
Affiliations:
Hampshire College, Amherst, MA, USA;SUNY New Paltz, New Paltz, NY, USA;Hampshire College, Amherst, MA, USA;Hampshire College, Amherst, MA, USA;Hampshire College, Amherst, MA, USA
Venue:
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Year:
2008

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Abstract

We describe the application of genetic programming (GP) to a problem in pure mathematics, in the study of finite algebras. We document the production of human-competitive results in the discovery of particular algebraic terms, namely discriminator, Pixley, majority and Mal'cev terms, showing that GP can exceed the performance of every prior method of finding these terms in either time or size by several orders of magnitude. Our terms were produced using the ECJ and PushGP genetic programming systems in a variety of configurations. We compare the results of GP to those of exhaustive search, random search, and algebraic methods.