Employing partial metamodels for optimization with scarce samples

To deal with high-dimensional, computationally expensive and black-box optimization (HEB) problems, a Partial Metamodel-based Optimization (PMO) method using Radial Basis Function-High Dimensional Model Representation (RBF-HDMR) along with a moving cut-center strategy is developed. To reduce the exponentially increasing cost of building an accurate metamodel for high dimensional problems, partial RBF-HDMR models of selected design variables are constructed at every iteration in the proposed strategy based on sensitivity analysis. After every iteration, the cut center of RBF-HDMR is moved to the most recent optimum point in order to pursue the optimum. Numerical tests show that the PMO method in general performs better than optimization with a complete RBF-HDMR for high-dimensional problems in terms of both effectiveness and efficiency. To improve the performance of the PMO method, a trust region based PMO (TR-PMO) is developed. When the allowed number of function calls is scarce, TR-PMO has advantages over compared metamodel-based optimization methods. The proposed method was then successfully applied to an airfoil design problem. The use of a partial metamodel for the purpose of optimization shows promises and may lead to development of other novel algorithms.