Response surfaces with discounted information for global optima tracking in dynamic environments

Two new methods for incorporating old and recent information into a surrogate model in order to improve the tracking of the global optima of expensive black boxes are presented in this paper. The response surfaces are built using Gaussian processes fitted to data which is obtained through sequential sampling. The efficient global optimization (EGO) algorithm applied to the generated response surface is used to determine the next most promising sample (where the expected improvement is maximized). The goal is to find the global maxima of an expensive to evaluate objective function which changes after a given number of function evaluations with as few samples as possible. Exploiting old information in a discounted manner significantly improves the search, which is shown through numerical experiments performed using the moving peaks benchmark (MPB)