Controlling mutation/selection algorithms with stochastic approximation

The article describes a stochastic approximation method to deal with adaptation in the mutation/selection strategy. Small mutation probabilities are considered. First, the convergence rate of the population Markov chain toward equilibrium is given. This result allows control of the number of generations sufficient to reach the stationary probability distribution. Under stationarity, the algorithm proceeds with the adaptation of a parameter called mutation radius. The main issue is the initialization of the adaptation process. The article gives a rule to initialize this process for simple one-dimensional problems. This initialization guarantees both the convergence of the adaptation scheme, and that an accurate solution is produced