Geodesic
Application of the lower-bound function method to the investigation of the convergence of genetic algorithms
Mathematica Applicanda, Tome 35 (2007) no. 49/08, pp. 33-45.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Markovian operators, non-negative linear operators and its subgroups play a significant role for the description of phenomena observed in the nature. Research on asymptotic stability is one of the main issues in this respect. A. Lasota and J. A. Yorke proved in 1982 that the necessary and sufficient condition of the asymptotic stability of a Markovian operator is the existence of a non-trivial lower-bound function. In the present paper it is shown how the method of lower-bound function can be applied to the investigation of genetic algorithms. Genetic algorithms considered used for solving of non-smooth optimization problems are compositions of two random operators: selection and mutation. The compositions are Markovian matrices.
DOI : 10.14708/ma.v35i49/08.1385
Classification : 68T05 (68W40)
Mots-clés : Markov operator, exponential stationarity, lower-bound function, genetic algorithm, mutation, selection 
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Jolanta Socała; Witold Kosiński. Application of the lower-bound function method to the investigation of the convergence of genetic algorithms. Mathematica Applicanda, Tome 35 (2007) no. 49/08, pp.  33-45. doi : 10.14708/ma.v35i49/08.1385. http://geodesic.mathdoc.fr/articles/10.14708/ma.v35i49/08.1385/

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