Globalization and parallelization of nelder-mead and powell optimization methods

Abstract

Optimization problems in engineering involve very often nonlinear functions with multiple minima or discontinuities, or the simulation of a system in order to determine its parameters. Global search methods can compute a set of points and provide alternative design answers to a problem, but are computationally expensive. A solution for the CPU dependency is parallelization, which leads to the need to control the sampling of the search space. This paper presents a parallel implementation of two free-derivative optimization methods (Nelder-Mead and Powell), combined with two restart strategies to globalize the search. The first is based on a probability density function, while the second uses a fast algorithm to uniformly sample the space. The implementation is suited to a faculty network, avoiding special hardware requirements, complex installation or coding details. © Springer Science+Business Media B.V. 2008.