The Simple Genetic Algorithm and the Walsh Transform: Part II, The Inverse | Zendy

Michael D. Vose | Zendy; Alden H. Wright | Zendy

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The Simple Genetic Algorithm and the Walsh Transform: Part II, The Inverse

Author(s) -

Michael D. Vose,

Alden H. Wright

Publication year - 1998

Publication title -

evolutionary computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 82

eISSN - 1530-9304

pISSN - 1063-6560

DOI - 10.1162/evco.1998.6.3.275

Subject(s) - crossover , mathematics , mixing (physics) , simple (philosophy) , mutation , inverse , operator (biology) , algorithm , population , zero (linguistics) , point (geometry) , genetic algorithm , scheme (mathematics) , combinatorics , mathematical optimization , mathematical analysis , computer science , artificial intelligence , genetics , physics , biology , philosophy , linguistics , geometry , demography , epistemology , repressor , quantum mechanics , sociology , transcription factor , gene

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.

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