Document Type

Article

Publication Title

Evolutionary Computation

Publisher

Massachusetts Institute of Technology Press

Publication Date

1998

Abstract

This paper is the first part of a two-part series. It proves a number of direct relationships between the Fourier transform and the simple genetic algorithm. (For a binary representation, the Walsh transform is the Fourier transform.) The results are of a theoretical nature and are based on the analysis of mutation and crossover. The Fourier transform of the mixing matrix is shown to be sparse. An explicit formula is given for the spectrum of the differential of the mixing transformation. By using the Fourier representation and the fast Fourier transform, one generation of the infinite population simple genetic algorithm can be computed in time O(cl log2 3), where c is arity of the alphabet and l is the string length. This is in contrast to the time of O(c3l) for the algorithm as represented in the standard basis. There are two orthogonal decompositions of population space that are invariant under mixing. The sequel to this paper will apply the basic theoretical results obtained here to inverse problems and asymptotic behavior.

DOI

10.1162/evco.1998.6.3.253

Comments

The Simple Genetic Algorithm and the Walsh Transform: part I: Theory, (with Michael D. Vose), Evolutionary Computation 6 (3), 1998, pages 253-274. View original published citation at 10.1162/evco.1998.6.3.253.

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