Intruder detection and interdiction modeling: A bilevel programming approach for ballistic missile defense asset location

Abstract

A relevant, applied problem in the location analysis literature is the effective location and allocation of resources to detect and interdict intruders traversing a defended region. For selected applications, defender resources are designed to detect and/or interdict intruders on specific parts (or stages) of the respective paths. Within this context, this research is motivated by the problem of effectively defending a set of population centers against attack by a limited number of intercontinental ballistic missiles (i.e., intruders). Herein, the defensive actions entail the location of ballistic missile defense resources to detect and interdict missiles over a range of possible launch-to-target missile paths and their respective, spatio-temporally defined stages of flight. Assumed is an adversary capability to observe the defensive asset locations and respond with an intercontinental ballistic missile targeting strategy that maximizes the expected damage of an attack. The research presents a bilevel programming model for the corresponding Stackelberg game and, via transformations and reformulations, identifies a single-objective mixed-integer nonlinear program that can be addressed with any of several commercially available solvers. Upon proving the convexity of the resulting formulation to assure reported solutions are globally optimal, comparative testing identifies the commercial solver ANTIGONE as preferred for solving instances of the underlying problem. Empirical testing via a designed experiment examines which scenario features of the underlying problem are most significant for predicting the required computational effort to solve problem instances, yielding insight into the practical nature of this research to address instances of increasing size.