Simulation-optimization studies: under efficient stimulation strategies, and a novel response surface methodology algorithm

Abstract

While attempting to solve optimization problems, the lack of an explicit mathematical expression of the problem may preclude the application of the standard methods of optimization which prove valuable in an analytical framework. In such situations, computer simulations are used to obtain the mean response values for the required settings of the independent variables. Procedures for optimizing on the mean response values, which are in turn obtained through computer simulation experiments, are called simulation-optimization techniques.

The focus of this work is on the simulation-optimization technique of response surface methodology (RSM). RSM is a collection of mathematical and statistical techniques for experimental optimization. Correlation induction strategies can be employed in RSM to achieve improved statistical inferences on experimental designs and sequential experimentations. Also, the search procedures currently employed by RSM algorithms can be improved by incorporating gradient deflection methods.

This dissertation has three major goals: (a) develop analytical results to quantitatively express the gains of using the common random number (CRN) strategy of variance reduction over direct simulation (independent streams or IS strategy) at each stage RSM, (b) develop a new RSM algorithm by incorporating gradient deflection methods in existing RSM algorithms, and (c) to conduct extensive empirical studies to quantify: (i) the use of eRN strategy over direct simulation in a standard RSM algorithm, and (ii) the gains of the new RSM algorithm over a standard existing RSM algorithm.