Considerations of Accuracy and Uncertainty with Kriging Surrogate Models in Single-Objective Electromagnetic Design Optimization

Abstract

The high computational cost of evaluating objective functions in electromagnetic optimal design problems necessitates the use of cost-effective techniques. This paper discusses the use of one popular technique, surrogate modelling, with emphasis placed on the importance of considering both the accuracy of, and uncertainty in, the surrogate model. After briefly reviewing how such considerations have been made in the single-objective optimization of electromagnetic devices, their use with kriging surrogate models is investigated. Traditionally, space-filling experimental designs are used to construct the initial kriging model, with the aim to maximize the accuracy of the initial surrogate model, from which the optimization search will start. Utility functions, which balance the predictions made by this model with its uncertainty, are often used to select the next point to be evaluated. In this paper, the performances of several different utility functions are examined using experimental designs which yield initial kriging models of varying degrees of accuracy. It is found that no advantage is necessarily achieved through searching for optima using utility functions on initial kriging models of higher accuracy, and that a reduction in the total number of objective function evaluations may be achieved by starting the iterative optimization search earlier with utility functions on kriging models of lower accuracy. The implications for electromagnetic optimal design are discussed