A modified stochastic response surface algorithm for expensive black-box global optimization

Abstract

In this paper, a modified stochastic response surface algorithm is proposed for solving expensive black-box global optimization problems. A counter to counts the consecutive failed iterations is used to guide the algorithm to enter into the local search phase or the global search phase accordingly. In the local search phase, the obtained global minimizer of the current response surface model will be taken as the new iteration point if certain conditions are satisfied, otherwise the new iteration point will be taken from some normally distributed random trial points generated around the obtained global minimizer of the current response surface model. In the global search phase, the new iteration point will be taken from some uniformly distributed random trial points on the feasible region. A restarting version of the algorithm is also discussed. Some numerical examples are given to show the effectiveness of the present algorithm.