Surrogate-based Optimization with Parallel Simulations using the Probability of Improvement

In surrogate-based optimization, each cycle consists of carrying out a number of simulations, fitting a surrogate, performing optimization based on the surrogate, and finally running exact simulation at the candidate solutions. Adaptive sampling algorithms that add one point per cycle are readily available. For example, the efficient global optimization (EGO) algorithm uses the kriging prediction and uncertainty estimate to guide the selection of the next sampling point. However, the addition of one point at a time may not be efficient when it is possible to run simulations in parallel. Additionally, the extension to include multiple points per cycle turns out to be either limited or computationally challenging. We propose an algorithm for adding several points per optimization cycle based on approximated computation of the probability of improvement. We assume that the probabilities at different points of the design space are independent from each other. The approach was tested on three analytic examples. For these examples we compare our approach with traditional sequential optimization based on kriging. We found that indeed our approach was able to deliver better results in a fraction of the optimization cycles needed by the traditional kriging implementation.