Robust Decision Making: Addressing Uncertainties in Distributions

Abstract

The public reporting burden for this collection of information is estimated to average 1 hour per response, including ■ gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Servic 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be awars that notwiths penalty for failing to comply with a collection of information if it does not display a currently valid 0MB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.AFRL-SR-AR-TR-04- PERFORMING ORGANIZATION NAME{S) AND ADDRESS(ES)University of Florida 310 Weil Hall Gainesville, FL 32611-6550 SPONSORING/MONITORING AGENCY NAME{S) AND ADDRESS(ES)Air SummaryThe project was concentrated on development of new methodologies for decision making in uncertain environment and relevant applications. The first part of the project was focused on analytical and discrete optimization approaches for routing an aircraft in threat environment. The model considered aircraft trajectory in three-dimensional space. Several threats were studied, including risk of aircraft detection by radars, sensors, and the risk of being killed by surface to air missiles. The problem of finding aircraft optirhal risk trajectory subject to a constraint on the trajectory length was solved by analytical and discrete optimization approaches.The second part of the project resulted in general approach to risk management for the case with uncertainties in distributions. The risk of loss, damage, or failure was measured by the Conditional Value-at-Risk (CVaR) measure. As a function of decision variables, CVaR is convex, and therefore can be efficiendy controlled/optimized using convex or linear programming. The methodology was tested on two Weapon-Target Assignment (WTA) problems. The total cost of a mission was minimized, while satisfying the operational constraints and ensuring destruction of targets with high probability. The risk of a failure of the mission is controlled by CVaR constraints. The case studies showed that there were significant qualitative and quantitative differences in solutions of deterministic and stochastic WTA problems.The third part of the project studied the Multiple Traveling Salesmen Problem (Multiple-TSP) in several variations. The research was focused on MIN-MAX 2-TSP, which cannot be solved by standard methods. The relation between this class of problems and a subclass of the self-dual monotonic Boolean functions was established. This resulted in new efficient optimization algorithms.