Document Type

Article

Publication Title

Evolutionary Computation

Publisher

Massachusetts Institute of Technology Press

Publication Date

1998

Volume

6

Issue

3

Disciplines

Computer Sciences

Abstract

This paper continues the development, begun in Part I, of the relationship between the simple genetic algorithm and the Walsh transform. The mixing scheme (comprised of crossover and mutation) is essentially “triangularized” when expressed in terms of the Walsh basis. This leads to a formulation of the inverse of the expected next generation operator. The fixed points of the mixing scheme are also determined, and a formula is obtained giving the fixed point corresponding to any starting population. Geiringer's theorem follows from these results in the special case corresponding to zero mutation.

Keywords

Random heuristic search, Geiringer’s theorem, Walsh transform, Fourier transform

DOI

10.1162/evco.1998.6.3.275

Comments

The Simple Genetic Algorithm and the Walsh Transform: part II: The Inverse, (with Michael D. Vose), Evolutionary Computation 6 (3), 1998, pages 275-289. View original published article at 10.1162/evco.1998.6.3.275.

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