Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999
Association of Mizar Users
Basic Properties of Genetic Algorithm

Akihiko Uchibori

Yamaguchi University, Ube

Noboru Endou

Shinshu University, Nagano
Summary.

We defined the set of the gene, the space treated by the genetic
algorithm and
the individual of the space. Moreover, we defined some genetic operators
such as one point crossover and two points crossover, and the validity
of many characters were proven.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[8]
[1]
[3]
[9]
[2]
[6]
[5]
[4]

Definitions of GeneSet, GASpace and Individual

Definitions of Several Genetic Operators

Properties of 1point Crossover

Properties of 2points Crossover

Properties of 3points Crossover

Properties of 4points Crossover

Properties of 5points Crossover

Properties of 6points Crossover
Bibliography
 [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Agata Darmochwal and Yatsuka Nakamura.
The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs.
Journal of Formalized Mathematics,
3, 1991.
 [5]
Jaroslaw Kotowicz.
Functions and finite sequences of real numbers.
Journal of Formalized Mathematics,
5, 1993.
 [6]
Andrzej Nedzusiak.
$\sigma$fields and probability.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received April 24, 1999
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