On Asymptotic Behaviour of a Simple Genetic xsAlgorithm

  • Witold Kosiński
  • Stefan Kotowski
  • Jolanta Socała
Part of the Advances in Soft Computing book series (AINSC, volume 35)


The simple genetic algorithm (SGA) and its convergence analysis are main subjects of the article. The SGA is defined on a finite multi-set of potential problem solutions (individuals) together with random mutation and selection operators. The selection operation acts on the basis of the fitness function defined on potential solutions (individuals), and is fundamental for the problem considered. Generation of a new population from the given one, is realized by the iterative actions of those operators. Each iteration is written in the form of a transition operator acting on probability vectors which describe probability distributions of each population. The transition operator is a Markov one. Thanks to the well-developed theory of Markov operators [5,8,9] new conditions for stability of the transition operator are formulated. The obtained results are related to the class of genetic operators and are not restricted to binary operators.


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Copyright information

© Springer 2006

Authors and Affiliations

  • Witold Kosiński
    • 1
    • 2
  • Stefan Kotowski
    • 3
  • Jolanta Socała
    • 4
  1. 1.Research Center, Department of Intelligent SystemsPolish-Japanese Institute of Information TechnologyWarszawaPoland
  2. 2.Institute of Environmental Mechanics and Applied Computer Science Kazimierz Wielki UniversityBydgoszczPoland
  3. 3.IPPT PANInstitute of Fundamental Technological ResearchWarszawaPoland
  4. 4.Institute of MathematicsSilesian UniversityKatowicePoland

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