Research Activities
My research interests are in the field of Operations
Research, with a focus on ergodic theory and discrete optimization (analysis
and heuristics). In particular, I
enjoy applying the techniques of Operations Research to a variety of fields and
applications. To achieve this, I have
participated in a variety of projects.
The following is a list of projects that I am currently involved in.
Projection Pursuit
The objective of this research
is to study the problem of finding an optimal projection of data contained in a
high dimensional space to a lower dimensional space. The data is partitioned into sets, where the sets represent the
origin of the data (where the data came from).
Optimality, in this case, will preserve the separation of the data. The Bayes Classifier is used to classify the
data in the low dimensional space.
Hybrid Local Search Algorithms
This research develops hybrid
local search algorithms for approaching discrete optimization problems. The idea is to merge convergent local search
algorithms (e.g., simulated annealing) with non-convergent algorithms (e.g.,
pure local search, Monte Carlo search).
Thereby, creating algorithms that combine heuristic procedures that
guarantee long term convergence (globally optimal solutions) with heuristic
procedures that guarantee reasonable finite-time performance (locally optimal
solutions).
Collaborators: Sheldon H.
Jacobson
Discrete Manufacturing Process Design
Optimization*
The goal of this research is
to construct efficient and effective optimization algorithms to identify
optimal/near-optimal manufacturing process designs, where the finished unit
meets certain geometric and microstructural specifications, and is produced at
minimum cost. Computer simulation
models of the manufacturing process designs are provided by the Materials
Process Design Branch of the Air Force Research Laboratory, Wright Patterson
Air Force Base (Dayton, Ohio, USA).
Collaborators: Derek Armstrong, Sheldon H. Jacobson, Kelly Sullivan and Allan
Johnson
Papers: Vaughan, D.E.,
Jacobson, S.H. and Armstrong, D. (2000)
Simultaneous
Generalized Hill Climbing Algorithms*
This
research focuses on approaching sets of related discrete optimization problems
(i.e., overlapping traveling salesman problems, machine shop scheduling
problems with similar constraints). The
aim of the research is to develop an algorithm that can approach the whole set
in one application. Information gained
while optimizing over one discrete optimization problem is used to initialize
in the subsequent discrete optimization problem.
Collaborators: Sheldon H. Jacobson
Papers: Vaughan, D.E. and
Jacobson, S.H. (2001b, 2001c)
Formulating the Meta-Heuristic Tabu Search
The goal of this project is
to mathematically formulate probabilistic tabu search to be used in conjunction
with other heuristics (i.e., simulated annealing). The framework allows the algorithm to be modeled using nonstationary
Markov chain theory. This framework
allows already existing convergence theories to embody applications of tabu
search.
Collaborators: Sheldon H. Jacobson
Papers: Vaughan, D.E. and
Jacobson, S.H. (2001a)
Optimal Search Strategy Problem*
This research models optimal
strategies for conducting military searches using a set of platforms (i.e.,
helicopters, planes) as the well-known traveling salesman problem. Local search algorithms as well as simultaneous
generalized hill climbing algorithms are used to approach these problems.
Collaborators:
Darrall Henderson, Sheldon H. Jacobson
Papers: Henderson, D.,
Vaughan, D.E., Jacobson, S.H. and Wakefield, R. (2001a)
Vaughan, D.E., Henderson, D. and Jacobson, S.H.
(2001)
Optimal
Earthmoving Vehicle Routes
This research develops a
mathematical model for minimizing the cost of operating large capacity vehicles
to level project sites prior to a construction project. The model is shown to be NP-hard and
approached using heuristics. This
research will aid in future collaboration between the field of operation
research and the field of construction engineering.
Collaborators: Darrall Henderson, Ron Wakefield, Sheldon H. Jacobson
Papers: Henderson, D., Wakefield, R., Vaughan, D.E.
and Jacobson, S.H. (2001b)
Henderson, D., Vaughan, D.E., Jacobson, S.H.,
Wakefield, R. and Sewell, E.C. (2001)
Analysis of the Urn Problem
This research uses
probability theory as well as computational techniques to approach variations
of the well-known urn problem.
Collaborators: John E. Kobza, Sheldon H. Jacobson
Papers: Vaughan, D.E., Kobza, J. and Jacobson, S.H.
(2001)
Hybrid Neighborhood Functions
This research develops
hybrid neighborhood functions for approaching discrete optimization
problems. Particular focus is on the
traveling salesman problem. So far a
hybrid neighborhood function has been developed that combines the 2-opt and
4-exchange neighborhood functions.
Collaborators: Sheldon H. Jacobson, Darrall Henderson
Papers: Vaughan, D.E., Henderson, D., Jacobson, S.H.
(2001)
*This work is supported in part by the Air Force
Office of Scientific Research (F49620-01-1-0007, F49620-98-1-0432) and the
National Science Foundation (DMI-9907980).