Stochastic optimization of control parameters in genetic algorithms

The genetic search can be modeled as a controlled Markovian process, the transition of which depends on control parameters (probabilities of crossover and mutation). This paper proposes a stochastic gradient and develops a stochastic approximation algorithm to optimize control parameters of genetic algorithms (GAs). The optimal values of control parameters can be found from a recursive estimation of control parameters provided by the stochastic approximation algorithm. The algorithm performs in finding a stochastic gradient of a given performance index and adapting the control parameters in the direction of descent. Numerical results based on the classical multimodal functions are given to show the effectiveness of the proposed algorithm.