Polynomial-chaos-kriging-assisted efficient global optimization

In this paper, we explore the use of the recently proposed polynomial chaos-Kriging (PCK) surrogate model to assist a single-objective efficient global optimization (EGO) framework in order to solve expensive optimization problems. PCK is a form of universal Kriging (UK) that employs orthogonal polynomials and least-angle-regression (LARS) algorithm to select the proper set of polynomial basis. The use of LARS within the PCK algorithm eliminates the need for the manual selection of UK's trend function. Investigation on the capability of PCK-EGO is performed on five synthetic and one aerodynamic test problems. In light of the results, we observe that PCK-EGO performs in a similar way to standard EGO in cases with no clear polynomial-like trend. However, PCK-EGO shows a notable faster convergence in problems where the objective function exhibits a landscape trend that can be captured by polynomials. Application to the subsonic wing problem further demonstrates that PCK-EGO is more efficient than EGO in a real-world aerodynamic optimization problem.