Date of Award
Master of Science in Operations Research
Department of Operational Sciences
Brian J. Lunday, PhD.
The Unites States and its allies confront a persistent and evolving threat from missile attacks as nations around the world continue to invest and advance their current capabilities. Within the air defense context of a missile-and-interceptor engagement, a challenge for the defender is that surface to air interceptor missile batteries often must be located to protect high-value targets dispersed over a vast area, subject to an attacker observing the disposition of batteries prior to developing and implementing an attack plan. To model this scenario, we formulate a two-player, three-stage, perfect information, sequential move, zero-sum game that accounts for, respectively, a defender's location of batteries, an attacker's launch of missiles against targets, and a defender's assignment of interceptors to incoming missiles. The resulting trilevel math programming formulation cannot be solved via direct optimization and it is not suitable to solve via full enumeration for realistically-sized instances. We instead utilize the game tree search technique Double Oracle, within which we embed alternative heuristics to solve an important subproblem for the attacker. We test and compare these solution methods to solve a designed set of 26 instances of parametric variation, from which we derive insights regarding the nature of the underlying problem. Whereas full enumeration required up to 8.6 hours to solve the largest instance considered, our superlative implementation of Double Oracle terminates in a maximum of 3.39 seconds over the set of instances, with an average termination time of less than one second. Double Oracle also properly identifies the optimal SPNE strategies in 75% of our test instances and, regarding those instances for which Double Oracle failed, we note that the relative deviation is less than 2.5% from optimal, on average, yielding promise as a solution method to solve realistically-sized instances.
DTIC Accession Number
Boardman, Nicholas T., "Heterogeneous Air Defense Battery Location: A Game Theoretic Approach" (2016). Theses and Dissertations. 354.