Optimization for Black-box Objective Functions

In many practical engineering design problems, the form of objective functions is not given explicitly in terms of design variables. Given the value of design variables, under this circumstance, the value of objective functions is obtained by real/computational experiments such as structural analysis, fluidmechanic analysis, thermodynamic analysis, and so on. Usually, these experiments are considerably expensive. In order to make the number of these experiments as few as possible, optimization is performed in parallel with predicting the form of objective functions. Response Surface Methods (RSM) are well known along this approach. This paper presents a brief review machine learning approaches to RSM such as Radial Basis Function Networks (RBFN) and Support Vector Machines (SVM). One of the most important tasks in this approach is to find effective sample data moderately in order to make the number of experiments as small as possible. Several methods are compared along with numerical examples.