Controlled Random Search Methods as a Stochastic Decision Process

As already discussed in the preceding chapter, in order to develop procedures for increasing the rate of convergence of the basic search method, the stochastic search procedure is equipped with a mechanism for controlling the conditional probability distributions of the search variates at the iteration points, generating the new trial points for improving the current iteration point. In an attendant control or stochastic decision process, the parameters of the search variables can be selected to maximize criteria for measuring the progress of the search, such as the probability of a step into the area of success, or the mean step length into the area of success at a certain iteration point. Due to the black-box situation concerning the objective function F, we have a stochastic control or decision process under uncertainty concerning the objective function. Based on a Bayesian approach, with the obtained information from the search algorithm, the conditional distribution of F, given the information obtained during the search, can be determined.