  In this paper, we investigate the capability of the universal Kriging (UK)
model for single-objective global optimization applied within an efficient
global optimization (EGO) framework. We implemented this combined UK-EGO
framework and studied four variants of the UK methods, that is, a UK with a
first-order polynomial, a UK with a second-order polynomial, a blind Kriging
(BK) implementation from the ooDACE toolbox, and a polynomial-chaos Kriging
(PCK) implementation. The UK-EGO framework with automatic trend function
selection derived from the BK and PCK models works by building a UK surrogate
model and then performing optimizations via expected improvement criteria on
the Kriging model with the lowest leave-one-out cross-validation error. Next,
we studied and compared the UK-EGO variants and standard EGO using five
synthetic test functions and one aerodynamic problem. Our results show that the
proper choice for the trend function through automatic feature selection can
improve the optimization performance of UK-EGO relative to EGO. From our
results, we found that PCK-EGO was the best variant, as it had more robust
performance as compared to the rest of the UK-EGO schemes; however, total-order
expansion should be used to generate the candidate trend function set for
high-dimensional problems. Note that, for some test functions, the UK with
predetermined polynomial trend functions performed better than that of BK and
PCK, indicating that the use of automatic trend function selection does not
always lead to the best quality solutions. We also found that although some
variants of UK are not as globally accurate as the ordinary Kriging (OK), they
can still identify better-optimized solutions due to the addition of the trend
function, which helps the optimizer locate the global optimum.
