Multi-Level Multi-Objective Programming and Optimization for Integrated Air Defense System Disruption

The U.S. military\u27s ability to project military force is being challenged. This research develops and demonstrates the application of three respective sensor location, relocation, and network intrusion models to provide the mathematical basis for the strategic engagement of emerging technologically advanced, highly-mobile, Integrated Air Defense Systems. First, we propose a bilevel mathematical programming model for locating a heterogeneous set of sensors to maximize the minimum exposure of an intruder\u27s penetration path through a defended region. Next, we formulate a multi-objective, bilevel optimization model to relocate surviving sensors to maximize an intruder\u27s minimal expected exposure to traverse a defended border region, minimize the maximum sensor relocation time, and minimize the total number of sensors requiring relocation. Lastly, we present a trilevel, attacker-defender-attacker formulation for the heterogeneous sensor network intrusion problem to optimally incapacitate a subset of the defender\u27s sensors and degrade a subset of the defender\u27s network to ultimately determine the attacker\u27s optimal penetration path through a defended network

Estimating the Probability of Being the Best System: A Generalized Method and Nonparametric Hypothesis Test

This thesis provides two new approaches for comparing competing systems. Instead of making comparisons based on long run averages or mean performance, the first paper presents a generalized method for calculating the probability that a single system is the best among all systems in a single trial. Unlike current empirical methods, the generalized method calculates the exact multinomial probability that a single system is best among competing systems. The ability to avoid time consuming empirical estimate techniques could potentially result in significant savings in both time and money when comparing alternate systems. A Monte Carlo simulation is conducted comparing the empirical probability estimates of the generalized integral method, calculated using a bootstrapping procedure and density estimation technique, with those of two related estimation techniques, Procedure BEM (Bechhofer, Elmaghraby, and Morse) and Procedure AVC (All Vector Comparisons). All test cases show comparable performance in empirical estimation accuracy of the generalized integral method with that of the current methods analyzed. The second paper proposes the use of a distribution-free ordered comparisons procedure to test whether one population is stochastically larger (or smaller) than the other. This procedure is suggested as a useful alternative to the well-known Wilcoxon rank sum and Mann-Whitney tests. A Monte Carlo study is conducted, comparing the methods based on simulated power and type I error. All test cases show a marked improvement in performance of the ordered comparisons test versus the Wilcoxon rank sum test, when testing for stochastic dominance. A table of critical values is presented and a large sample approximation is given