Considerations of accuracy and uncertainty with kriging surrogate models in single-objective electromagnetic design optimisation

The high computational cost of evaluating objective functions in electromagnetic optimum design problems necessitates the use of cost-effective techniques. The 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 a brief review of how such considerations have been made in the single-objective optimisation 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 of maximising the accuracy of the initial surrogate model, from which the optimisation 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, with experimental designs that yield initial kriging models of varying degrees of accuracy. It is found that no advantage is necessarily achieved through a search for optima using utility functions on initial kriging models of higher accuracy, and that a reduction in the total number of objective function evaluations can be achieved if the iterative optimisation search is started earlier with utility functions on kriging models of lower accuracy. The implications for electromagnetic optimum design are discussed.