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.

MML Identifier: GENEALG1

The terminology and notation used in this paper have been introduced in the following articles [7] [8] [1] [3] [9] [2] [6] [5] [4]

Contents (PDF format)

  1. Definitions of Gene-Set, GA-Space and Individual
  2. Definitions of Several Genetic Operators
  3. Properties of 1-point Crossover
  4. Properties of 2-points Crossover
  5. Properties of 3-points Crossover
  6. Properties of 4-points Crossover
  7. Properties of 5-points Crossover
  8. Properties of 6-points 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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