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Multistage Markov Chain Modeling of the Genetic Algorithm and Convergence Results |
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| Authors: | Chang C. Y. Dorea Judinor A. Guerra Jr. Rafael Morgado Andre G. C. Pereira |
| Affiliation: | 1. Department of Mathematics , Universidade de Brasilia , Brasilia DF, Brazil changdorea@unb.br;3. Department of Electrical Engineering/Department of Mathematics , Universidade Federal do Rio Grande do Norte , Natal, RN, Brazil;4. Department of Mathematics , Universidade de Brasilia , Brasilia DF, Brazil |
| Abstract: | The genetic algorithm (GA) has been widely used to solve combinatorial global optimization problems. Despite the successes that GA encounters in practical applications, there exist few precise results on its behavior. In this article, we formulate a fully rigorous mathematical modeling of GA as a multistage Markov chain and derive convergence results. Variations that include the simulated annealing algorithm and the GA with superindividual are considered. |
| Keywords: | Genetic algorithm Global optimization Simulated annealing |