An efficient simplex-based method for solving large linear programs

Simple item page
dc.contributor.advisorBixby, Robert E.en_US
dc.creatorDadmehr, Shireen Saraen_US
dc.date.accessioned2009-06-04T00:05:18Zen_US
dc.date.available2009-06-04T00:05:18Zen_US
dc.date.issued1995en_US
dc.description.abstractA simplex-based method of solving specific classes of large-scale linear programs is presented. The structure of both staircase and block-angular linear programs is exploited to construct an advanced or "crash" basis to be used with a simplex-based linear program solver. First, the constraint matrix is decomposed into blocks. In contrast to many other systems that require additional information about the form of the linear program, the method described here determines this decomposition without prior knowledge of the matrix structure. As the problem of automatically finding such a decomposition is NP-complete, a heuristic is used to discover blocks within the constraint matrix. After a decomposition of the constraint matrix is determined, smaller linear programs called subproblems are formed. These subproblems are solved using a simplex-based solver, and the solution information is used to construct an advanced or "crash" basis for the original linear program. In contrast to decomposition methods that iteratively solve subproblems to obtain a solution to the original problem, this approach requires solving each subproblem at most twice. Finally, the original linear program is solved by providing the advanced basis to a simplex-based solver. Results indicate that this method solves some large linear programs much faster than state-of-the-art simplex-based solvers do. For example, for a set of linear programs that range in size from 5,000 x 9,000 to 30,000 x 50,000 constraints and variables, the presented method solves each linear program in about a tenth the number of simplex iterations. This reduces the total time required to solve each linear program by a factor of from two to five.en_US
dc.format.extent110 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 1995 DADMEHRen_US
dc.identifier.citationDadmehr, Shireen Sara. "An efficient simplex-based method for solving large linear programs." (1995) Diss., Rice University. <a href="https://hdl.handle.net/1911/16813">https://hdl.handle.net/1911/16813</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/16813en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.titleAn efficient simplex-based method for solving large linear programsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
9610632.PDF
Size:
3.55 MB
Format:
Adobe Portable Document Format
Download
Collections
Rice University Theses and Dissertations