Abstract

Computer simulations of complex physical phenomena are used in many contexts, including that of engineering design. Increasingly scientists and engineers have also been trying to optimize problems defined by such simulations (e.g. to determine design parameters for a physical product). However, these problems often have several features that hinder the use of standard optimization techniques. The lack of derivative information and numerical error induced by the simulation can cause problems for derivative-based optimization methods. Likewise, extreme computational expense can make the use of direct search methods problematic.

The Model-Assisted Pattern Search (MAPS) algorithm, which is the subject of this research, attempts to address the issue. While maintaining a pattern search framework, MAPS makes use of easily constructed surrogates to the objective function in order to speed the optimization process. Numerical results for MAPS and several other algorithms are presented here for a variety of different objective functions.