Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. ; Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators. An original and crucial feature of the framework we propose is the mechanism of inter-deme agent operation synchronization. It is important from both a practical and a theoretical point of view. ; We show that under a mild assumption the resulting Markov chain is ergodic and the sequence of the related sampling measures converges to some invariant measure. The asymptotic guarantee of success is also obtained as a simple issue of ergodicity. Moreover, if the cardinality of each island population grows to infinity, then the sequence of the limit invariant measures contains a weakly convergent subsequence. ; The formal description of the island model obtained for the case of solving a single-objective problem can also be extended to the multi-objective case.
Oct 14, 2021
Sep 15, 2021
|The island model as a Markov dynamic system||Oct 14, 2021|
Kryazhimskii, Arkadii Triggiani, Roberto- ed. Maksimov, Vyacheslav I. - ed.
Styrcz, Anna Mrozek, Janusz Mazur, Grzegorz Korbicz, Józef - red. Uciński, Dariusz - red.
Batyrshin, Ildar Wagenknecht, Michael Rutkowska, Danuta - ed. Kacprzyk, Janusz - ed. Zadeh, Lotfi A. - ed.
Witkowska, Anna Śmierzchalski, Roman Cordón, Oskar - ed. Kazienko, Przemysław - ed.
Rodríguez, José M. Sofonea, Mircea - ed. Viano, Juan M. - ed.
El Mouatasim, Abdelkrim Ellaia, Rachid Souza de Cursi, Eduardo Korbicz, Józef - red. Uciński, Dariusz - red.
Kowalczuk, Zdzisław Suchomski, Piotr Białaszewski, Tomasz Korbicz, Józef - red. Patton, Ronald J. - red.
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