Efficient Global Optimization with Adaptive Target for Probability of Targeted Improvement

The use of Surrogate-based optimization has become increasingly prevalent in the design of engineering systems. Each optimization cycle consists of fitting a surrogate through an initial number of designs and performing optimization based on the surrogate to get a new design, where an exact simulation is performed. Algorithms like Efficient Global Optimization use uncertainty estimates available with the Kriging surrogate to guide the selection of new point(s). With access to parallel computation, adding multiple points per optimization cycle has become increasingly attractive. With EGO, Expected Improvement is commonly used as the criterion for selection of new point, but it is difficult and computationally expensive to add multiple points using this criterion. It is much easier to select multiple points when Probability of targeted Improvement is used as the selection criterion, but it suffers from the issue of target setting due to lack of knowledge of the true function. An adaptive target setting method is proposed in this paper, which changes the target to reflect the improvement achieved in each optimization cycle. This method is demonstrated to be highly efficient for three analytic examples. For these examples the proposed method is compared to a constant target setting and is shown to give better results. It is also seen that when multiple points are added per cycle using this method, the convergence rate becomes faster and also, the confidence in the final result becomes much higher.