Date of Award

3-2007

Document Type

Thesis

Degree Name

Master of Science in Operations Research

Department

Department of Operational Sciences

First Advisor

Mark A. Abramson, PhD

Second Advisor

James W. Chrissis, PhD

Third Advisor

Marcus B. Perry, PhD

Abstract

This research focuses on numerically solving a class of computationally expensive optimization problems that possesses a unique characteristic: as the optimal solution is approached, the computational time required to compute an objective function value decreases. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration and comparison process. The goal is to find the parameters of a predetermined image by comparing the flow dynamics from the numerical simulation and the predetermined image through the image comparison process. The generalized pattern search and mesh adaptive direct search methods were applied in a way that employs surrogate functions in the search step to reduce the number of costly function evaluations. The surrogate functions are formed, based on either previous function values or their computational times, or both. The solution to the surrogate optimization problem can be solved easily and provides an improved solution quickly. A time cut-off parameter was also added to the objective function to allow its termination during the comparison process if the computational time exceeded a specified threshold. The approach was tested on two problems using the NOMADm and DACE MATLAB® software packages, and results are presented.

AFIT Designator

AFIT-GOR-ENC-07-01

DTIC Accession Number

ADA465291

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