Global optimization of computationally expensive functions using serial and parallel radial basis function algorithms
Christine A. Shoemaker, Rommel G. Regis · 2004
This research develops and applies new algorithms for the global optimization of computationally expensive functions using radial basis function (RBF) models. The first contribution is CORS-RBF, an iterative RBF method where the next function evaluation point is a global minimum of the RBF model satisfying some distance constraints. CORS-RBF converges to the global minimum of an arbitrary continuous function defined over a compact set. Computational experiments indicate that two implementations of CORS-RBF are better than alternative methods on a nonlinearly constrained test problem and are comparable to alternatives on some box-constrained test problems. The second contribution is Stochastic RBF (Stoch-RBF), another iterative method where the next evaluation point is the best point from a set of randomly generated points which are ranked according to a weighted score based on an RBF criterion and a distance criterion. If the global minimizer of a continuous function is unique, Stoch-RBF converges almost surely to this point. Computational experiments indicate that two implementations of Stoch-RBF are superior to the RBF method by Gutmann (2001) (Gutmann-RBF) on several test functions and on a 12-dimensional groundwater bioremediation problem (GWB12). The third contribution includes some strategies for improving the performance of Gutmann-RBF and CORS-RBF when initialized by symmetric Latin hypercube designs. These strategies are complete restart and the restricted global minimization of the bumpiness function in Gutmann-RBF in some iterations. The fourth contribution is a framework for using local function approximation to enhance evolutionary optimization algorithms when applied to expensive functions. Computational experiments on several test functions and on GWB12 demonstrate that an evolution strategy can be enhanced by using local RBF models. The fifth contribution is the parallelization of Gutmann-RBF and CORS-RBF which resulted in good speedups on test problems when using up to 6 processors. The results show that neither Parallel Gutmann-RBF nor Parallel CORS-RBF dominates the other on all test problems and processor settings considered. The last contribution is MAPO-RBF, a parallel algorithm that uses a committee of RBF methods to generate several distinct points for simultaneous evaluation on multiple processors. Promising results for MAPO-RBF were obtained on several test functions and on GWB12.