Robust Decision Making: Addressing Uncertainties in Distributions
Abstract
The 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 optimal 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 efficiently 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 10, 2004
- Accession Number
- ADA423866
Entities
People
- Pãnos M. Pardalos
- Stanislav Uryasev
Organizations
- University of Florida