The effect of the type and parameter of the radial basis function on the performance of metamodel-based sequential global optimization

Abstract

Metamodel-based sequential global optimization (SGO) aims for finding the global optimum with a relatively small number of sample design points where expensive simulations are performed, and widely used for industrial design problems. As a metamodel-based SGO, “Constrained Optimization by Radial basis function interpolation” (COBRA) has been proposed using a cubic radial basis function (RBF) with a linear polynomial tail as a metamodel. In this study, we investigated the effect of the types and parameters of RBFs on the efficiency and robustness of COBRA by comparing numerical results on test problems consisting of four mathematical and three engineering problems which represent various optimization problems. The types of RBFs employed in this study were Gaussian, Multi-quadric, thin plate spline, and cubic. We also investigated the effect of the number of initial sample points on the performance of COBRA with varying it from NDV+1 to 10NDV where NDV denotes the number of design variables. Then, we recommended the type and parameter of the RBF that showed the best COBRA performance for the test problems. We recommended the Gaussian with r=10 for a relatively small number of initial sample points (more than or equal to 5NDV), and the Gaussian with r=5 for a relatively large number of initial sample points (less than or equal to 3NDV). The top three RBFs without regarding to the number of initial sample points were Multi-quadric with r=5, Gaussian with r=5, Multi-quadric with r=1