Pallage, Hiruni Kamali
(2019)
Optimization via Benders' Decomposition.
Master's Thesis, University of Pittsburgh.
(Unpublished)
Abstract
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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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
| Creators | Email | Pitt Username | ORCID  |
|---|
| Pallage, Hiruni Kamali | hkp7@pitt.edu | hkp7 | |
|
| ETD Committee: |
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| 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 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/37123 |
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