Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Mathematics and Statistics

First Advisor

Dursun A. Bulutoglu, PhD.


Modern statistical experiments routinely feature a large number of input variables that can each be set to a variety of different levels. In these experiments, output response changes as a result of changes in the individual factor level settings. Often, an individual experimental run can be costly in time, money or both. Therefore, experimenters generally want to gain the desired information on factor effects from the smallest possible number of experimental runs. Orthogonal arrays provide the most desirable designs. However, finding orthogonal arrays is a very challenging problem. There are numerous integer linear programming formulations (ILP) in the literature whose solutions are orthogonal arrays. Because of the nature of orthogonal arrays, these ILP formulations contain symmetries where some portion of the variables in the formulation can be swapped without changing the ILP. These symmetries make it possible to eliminate large numbers of infeasible or equivalent solutions quickly, thereby greatly reducing the time required to find all non-equivalent solutions to the ILPs. In this dissertation, a new method for identifying symmetries is developed and tested using several existing and new ILP formulations for enumerating orthogonal arrays.

AFIT Designator


DTIC Accession Number