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Two applications of combinatorial optimization

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Title
Two applications of combinatorial optimization
Name (type = personal)
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Oster
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Matthew R.
NamePart (type = date)
1983-
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Matthew Oster
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author
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Eckstein
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Jonathan
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Jonathan Eckstein
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Advisory Committee
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chair
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Alizadeh
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Farid Alizadeh
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internal member
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Boros
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Endre
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Endre Boros
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Advisory Committee
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BEN-ISRAEL
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ADI BEN-ISRAEL
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Advisory Committee
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Anjos
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Miguel
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Miguel Anjos
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Advisory Committee
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outside member
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Rutgers University
Role
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degree grantor
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Graduate School - New Brunswick
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Text
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theses
OriginInfo
DateCreated (qualifier = exact)
2014
DateOther (qualifier = exact); (type = degree)
2014-05
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
This thesis presents two applications of combinatorial optimization. The first part contains a detailed description of a conference scheduling problem. We model the problem as a symmetric clustering problem, or a variant of minimum k-partition we call capacitated k-partition. This problem is proved to be NP-hard to solve to optimality, and further, unless P = NP, no constant factor polynomial-time approximation algorithm exists. We also propose a branch-and-cut algorithm with semidefinite programming relaxations enhanced with polyhedral cuts found at each tree node. Many cutting planes are demonstrated to be satisfied, or provably close to being satisfied, by semidefinite matrices in the variable space [−1/(k − 1), 1], which is in contrast to basic linear programming relaxations. Our algorithm also relies on a novel heuristic strategy when attempting to generate feasible solutions at every tree node. We test an implementation of our algorithm on random k-partition instances as well as a particular conference data set which comes from the 13th Annual INFORMS Computing Society Conference and was solved to within 0.85% of optimum in under 4 hours. The results here are promising and provide a starting point for future projects. In the second part, we describe a project called the Boat Allocation Module, where a team comprised of United States Coast Guard (USCG) analysts, and Command, Control, and Interoperability Center for Advanced Data Analysis researchers worked together in building a decision support system for USCG analysts. The software was designed to solve the problem of allocating boats of the Coast Guard to the nation’s coastal stations, so as to meet station requirements, while adhering to particular budget and capability limitations. We model the problem as a resource allocation problem and prove that it is NP-hard to solve. We relax the problem slightly by allowing a single boat type to be shared, or assigned among disjoint subsets of stations rather than to individual stations, but show that implementing “seasonal” sharing is NP-hard. A mixed integer linear programming formulation is proposed, and an implementation within a decision support system for USCG analysts is tested as per USCG Verification and Validation standards. The software provides an intuitive interface and allows for a variety of scenarios. Tests have shown that our tool may save the Coast Guard millions of dollars a year.
Subject (authority = RUETD)
Topic
Operations Research
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Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_5344
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
xi, 148 p. : ill.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Matthew R. Oster
Subject (authority = ETD-LCSH)
Topic
Combinatorial optimization
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3SB4419
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
RightsHolder (type = personal)
Name
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Oster
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Matthew
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Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2014-04-04 03:09:29
AssociatedEntity
Name
Matthew Oster
Role
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Affiliation
Rutgers University. Graduate School - New Brunswick
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Type
License
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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Open
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windows xp
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