Robust Solutions to Uncertain Multiobjective Programs
Başlık:
Robust Solutions to Uncertain Multiobjective Programs
Yazar:
Dranichak, Garrett M., author.
ISBN:
9780438054431
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (276 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Margaret Wiecek Committee members: Warren Adams; Herve Kerivin; Matthew Saltzman; Cole Smith.
Özet:
Decision making in the presence of uncertainty and multiple conflicting objectives 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 incorporate 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 developed, 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.
Notlar:
School code: 0050
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
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XX(680242.1) | 680242-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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