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Optimization of control parameters in genetic algorithms: A stochastic approach. (English) Zbl 1020.65032
Summary: This paper proposes a stochastic approach for optimization of control parameters (probabilities of crossover and mutation) in genetic algorithms (GAs). The genetic search can be modelled as a controlled Markov process, the transition of which depends on the control parameters. A stochastic optimization problem is formed for control of GA parameters, based on a given performance index of populations and analysed as a controlled Markov process during the genetic search.
The optimal values of control parameters can be found from a recursive estimation of control parameters, which is obtained by introducing a stochastic gradient of the performance index and using a stochastic approximation algorithm. The algorithm possesses the capability of finding the stochastic gradient and adapting the control parameters in the direction of descent.
A non-stationary Markov model is developed to investigate asymptotic convergence properties of the proposed GA. It is proved that the proposed GA would asymptotically converge. Numerical results based on the classical functions are obtained to show the potential of the proposed algorithm.

65K05 Numerical mathematical programming methods
90C15 Stochastic programming
60J05 Discrete-time Markov processes on general state spaces
65C50 Other computational problems in probability (MSC2010)
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