| The task of optimally assigning military ordinance to enemy targets, often termed the Weapon Target Assignment (WTA) problem, has become a major focus of modern military thought. Current formulations of this problem consider the enemy targets as either passive or entirely defensive. As a result, the assignment problem is solved purely as a one sided team optimization problem. In practice, however, especially in environments characterized by the presence of an intelligent adversary, this one sided optimization approach has very limited use. The presence of an adversary often necessitates incorporating its intended actions in the process of solving the weapons assignment problem. In this dissertation, we formulate the weapon target assignment problem in the presence of an intelligent adversary within the framework of game theory. We consider two teams of opposing units simultaneously targeting each other and examine several possible game theoretic solutions of this problem. An issue that arises when searching for any solution is the dimensionality of the search space which quickly becomes overwhelming even for simple problems with a small number of units on each side. To solve this scalability issue, we present a novel algorithm called Unit Level Team Resource Allocation (ULTRA), which is capable of generating approximate solutions by searching within appropriate subspaces of the search space. We evaluate the performance of this algorithm on several realistic simulation scenarios. We also show that this algorithm can be effectively implemented in real-time as an automatic target assigning controller in a dynamic multi-stage problem involving two teams with large number of units in conflict. |
