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Empirical Analysis of Algorithms for Block-Angular Linear Programs

dc.contributor.authorDang, Jiarui
dc.date.accessioned2007-08-29T14:31:46Z
dc.date.available2007-08-29T14:31:46Z
dc.date.issued2007-08-29T14:31:46Z
dc.date.submitted2007
dc.description.abstractThis thesis aims to study the theoretical complexity and empirical performance of decomposition algorithms. We focus on linear programs with a block-angular structure. Decomposition algorithms used to be the only way to solve large-scale special structured problems, in terms of memory limit and CPU time. However, with the advances in computer technology over the past few decades, many large-scale problems can now be solved simply by using some general purpose LP software, without exploiting the problems' inner structures. A question arises naturally, should we solve a structured problem with decomposition, or directly solve it as a whole? We try to understand how a problem's characteristics influence its computational performance, and compare the relative efficiency of algorithms with and without decomposition. Two comparisons are conducted in our research: first, the Dantzig-Wolfe decomposition method (DW) versus the simplex method (simplex); second, the analytic center cutting plane method (ACCPM) versus the interior point method (IPM). These comparisons fall into the two main solution approaches in linear programming: simplex-based algorithms and IPM-based algorithms. Motivated by our observations of ACCPM and DW decomposition, we devise a hybrid algorithm combining ACCPM and DW, which are the counterparts of IPM and simplex in the decomposition framework, to take the advantages of both: the quick convergence rate of IPM-based methods, as well as the accuracy of simplex-based algorithms. A large set of 316 instances is incorporated in our experiments, so that different dimensioned problems with primal or dual block-angular structures are covered to test our conclusions.en
dc.identifier.urihttp://hdl.handle.net/10012/3189
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.subjectempirical analysisen
dc.subjectblock-angularen
dc.subjectDantzig-Wolfe decompositionen
dc.subjectanalytic center cutting plane methoden
dc.subjectinterior point methoden
dc.subjectsimplexen
dc.subject.programAccountingen
dc.titleEmpirical Analysis of Algorithms for Block-Angular Linear Programsen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentManagement Sciencesen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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