ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions

Abstract. We present a new derivative-free algorithm, ORBIT, for unconstrained local optimization of computationally expensive functions. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. The RBF models considered often allow ORBIT to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques. Approximation guarantees are obtained by ensuring that a subset of the interpolation points are sufficiently poised for linear interpolation. The RBF property of conditional positive definiteness yields a natural method for adding additional points. We present numerical results on test problems to motivate the use of ORBIT when only a relatively small number of expensive function evaluations are available. Results on two very different application problems, calibration of a watershed model and optimization of a PDE-based bioremediation plan, are also very encouraging and support ORBIT'...

• Type: Journal
• Year: 2008
• Where: SIAMSC
• Authors: Stefan M. Wild, Rommel G. Regis, Christine A. Shoemaker
• Keywords: Expensive Function, Function Evaluations, Radial Basis Functions, SIAMSC 2008