Date of Award


Document Type


Degree Name

Master of Science


Department of Operational Sciences

First Advisor

Brian J. Lunday, PhD


This research considers the problem of an intruder attempting to traverse a defender's territory in which the defender locates and employs disparate sets of resources to lower the probability of a successful intrusion. The research is conducted in the form of three related research components. The first component examines the problem in which the defender subdivides their territory into spatial stages and knows the plan of intrusion. Alternative resource-probability modeling techniques as well as variable bounding techniques are examined to improve the convergence of global solvers for this nonlinear, nonconvex optimization problem. The second component studies a similar problem but wherein the defender is unaware of the intrusion plan and may leverage dual purpose detection-and-interdiction resources. For the resulting nonconvex, multi-objective optimization problem, alternative solution methods are examined, benchmarking conceptually different multi-objective genetic algorithms against leading commercial solvers applied with conventional Pareto frontier exploration techniques. The third component further considers a game-theoretic framework in which the attacker observes a defender's location decisions prior to formulating an appropriate intrusion plan. For the resulting bilevel program, sequential relaxation and transformation yields a single-level, convex program for which the optimal solution is proven to be optimal to the original problem. Testing demonstrates the relative efficacy of this solution method for realistic problem sizes.

AFIT Designator


DTIC Accession Number