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Optimization via Benders' Decomposition

Pallage, Hiruni Kamali (2019) Optimization via Benders' Decomposition. Master's Thesis, University of Pittsburgh. (Unpublished)

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In a period when optimization has entered almost every facet of our lives, this thesis is designed to establish an understanding about the rather contemporary optimization technique: Benders' Decomposition. It can be roughly stated as a method that handles problems with complicating variables, which when temporarily fixed, yield a problem much easier to solve. We examine the classical Benders' Decomposition algorithm in greater depth followed by a mathematical defense to verify the correctness, state how the convergence of the algorithm depends on the formulation of the problem, identify its correlation to other well-known decomposition methods for Linear Programming problems, and discuss some real-world examples. We introduce present extensions of the method that allow its application to a wider range of problems. We also present a classification of acceleration strategies which is centered round the key sections of the algorithm. We conclude by illustrating the shortcomings, trends, and potential research directions.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Pallage, Hiruni Kamalihkp7@pitt.eduhkp7
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairWheeler, Jeffrey Pauljwheeler@pitt.edujwheeler
Committee MemberTrick, Michael
Committee MemberErmentrout, G. Bardbard@pitt.edubard
Committee MemberJason, DeBloisjdeblois@pitt.edujdeblois
Committee MemberMichael, Schneiermhs64@pitt.edumhs64
Date: 25 September 2019
Date Type: Publication
Defense Date: 12 July 2019
Approval Date: 25 September 2019
Submission Date: 18 July 2019
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 101
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: Optimization, Benders' Decomposition algorithm, Facility Location Problem, IMRT Treatment Planning, Partitioning Theorem, Multi step procedure, Mixed variables programming problem
Date Deposited: 25 Sep 2019 16:31
Last Modified: 25 Sep 2019 16:31


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