Optimization of control parameters in genetic algorithms: a stochastic approach

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 Markovian 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 Markovian process during the generic 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 genetic algorithm. It is proved that the proposed genetic algorithm would asymptotically converge. Numerical results based on the classical functions are obtained to show the potential of the proposed algorithm.