New models for homeland security and public safety

The standard approach to mathematical optimization is to construct models which assume 1) perfect knowledge of the algebraic form of the optimizable function, and 2) that the problem parameters are not subject to external random influences. In many practical settings, these assumptions are often too strong because even moderate amounts of randomness can lead to considerably sub-optimal outcomes. This dissertation examines three such problems within the general arena of public security, and proposes new mechanisms to cope with the underlying uncertainty involved in them. The first problem is a discrete optimization problem in which we seek (in the theater of battle) to properly configure a number of unmanned aerial vehicles subject to budget, weight, and size constraints. The objective is to select the best set of components so as to constitute a fleet which on average maximizes some payoff function whose closed algebraic form is unknown. To tackle this challenge, we introduce a new simulation-based heuristic that uses an adaptive criterion to sample the solution space, and efficiently distribute valuable simulation time among promising candidate solutions. The next problem is a patrol problem in which we need to allocate a budget resource both to the detection of illicit activity on some area of interest, and to the dispatching of patrol agents to disrupt or resolve those incidents. Moreover, these illegal activities are resolvable only before certain time deadlines that could be unknown. We show how to construct routes that guarantee minimum desired probabilities for resolving these incidents, and experimental results suggest that a larger budget can help neutralize the adverse impact of deadline uncertainty. The final problem entails an emergency response scenario in which aid workers tour relief centers while accumulating valuable relief supplies destined to serve deprived populations in the wake of a disaster. Situational urgency requires that these target populations be served before deadlines that are subject to random variation as new victims arrive. Moreover, potentially disruptive secondary disasters may also introduce randomness in the travel times on the paths between relief centers, and between relief centers and populations. We propose a new optimization framework to help these relief workers assess the value of routing options against the probabilities of these routes leading to missed deadlines (i.e., infeasibility risk). (Published By University of Alabama Libraries