Date of Award
Doctor of Philosophy (PhD)
Dr. Margaret Wiecek, Committee Chair
Dr. Warren Adams
Dr. Herve Kerivin
Dr. Matthew Saltzman
Dr. Cole Smith
Decision making in the presence of uncertainty and multiple conﬂicting objec-tives is a real-life issue, especially in the ﬁelds of engineering, public policy making, business management, and many others. The conﬂicting goals may originate from the variety of ways to assess a system’s performance such as cost, safety, and aﬀordability, while uncertainty may result from inaccurate or unknown data, limited knowledge, or future changes in the environment. To address optimization problems that incor-porate these two aspects, we focus on the integration of robust and multiobjective optimization. Although the uncertainty may present itself in many diﬀerent ways due to a diversity of sources, we address the situation of objective-wise uncertainty only in the coeﬃcients of the objective functions, which is drawn from a ﬁnite set of scenarios. Among the numerous concepts of robust solutions that have been proposed and de-veloped, we concentrate on a strict concept referred to as highly robust eﬃciency in which a feasible solution is highly robust eﬃcient provided that it is eﬃcient with respect to every realization of the uncertain data. The main focus of our study is uncertain multiobjective linear programs (UMOLPs), however, nonlinear problems are discussed as well. In the course of our study, we develop properties of the highly robust eﬃcient set, provide its characterization using the cone of improving directions associated with the UMOLP, derive several bound sets on the highly robust eﬃcient set, and present a robust counterpart for a class of UMOLPs. As various results rely on the polar and strict polar of the cone of improving directions, as well as the acuteness of this cone, we derive properties and closed-form representations of the (strict) polar and also propose methods to verify the property of acuteness. Moreover, we undertake the computation of highly robust eﬃcient solutions. We provide methods for checking whether or not the highly robust eﬃcient set is empty, computing highly robust eﬃcient points, and determining whether a given solution of interest is highly robust eﬃcient. An application in the area of bank management is included.
Dranichak, Garrett M., "Robust Solutions to Uncertain Multiobjective Programs" (2018). All Dissertations. 2154.