Structural Search Spaces and Genetic Operators

Autor:	Jonathan E. Rowe, Alden H. Wright, Michael D. Vose
Rok vydání:	2004
Předmět:	Discrete mathematics Pure mathematics Models Genetic Crossover Defining length Computational Mathematics symbols.namesake Fourier transform Matrix group Hadamard transform If and only if Schema (psychology) Mutation symbols Humans Crossing Over Genetic Abelian group Algorithms Mathematics
Zdroj:	Evolutionary Computation. 12:461-493
ISSN:	1530-9304 1063-6560
DOI:	10.1162/1063656043138941
Popis:	In a previous paper (Rowe et al., 2002), aspects of the theory of genetic algorithms were generalised to the case where the search space, Ω, had an arbitrary group action defined on it. Conditions under which genetic operators respect certain subsets of Ω were identified, leading to a generalisation of the termschema. In this paper, search space groups with more detailed structure are examined. We define the class of structural crossover operators that respect certain schemata in these groups, which leads to a generalised schema theorem. Recent results concerning the Fourier (or Walsh) transform are generalised. In particular, it is shown that the matrix group representing Ω can be simultaneously diagonalised if and only if Ω is Abelian. Some results concerning structural crossover and mutation are given for this case.
Databáze:	OpenAIRE
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