Relative Expected Improvement in Kriging Based Optimization

Global optimization is a common task in advanced engineering. The objective function can be very expensive to calculate or measure. In particular this is the case in Computational Fluid Dynamics (CFD) where simulations are extremely expensive and time-consuming. At present, the CFD code can also generate the exact derivatives of the objective function so we can use them in our models. The long computation to evaluate the objective function and (as a rule) high dimension of the design space make the optimization process very time-consuming. Widely adopted strategy for such objective functions is to use response function methodology.