Title:
Cutting Planes for Large Mixed Integer Programming Models

dc.contributor.advisor Cook, William J.
dc.contributor.author Goycoolea, Marcos G. en_US
dc.contributor.committeeMember Gu, Zonghao
dc.contributor.committeeMember Johnson, Ellis L.
dc.contributor.committeeMember Nemhauser, George L.
dc.contributor.committeeMember Thomas, Robin
dc.contributor.department Industrial and Systems Engineering en_US
dc.date.accessioned 2007-03-27T18:03:17Z
dc.date.available 2007-03-27T18:03:17Z
dc.date.issued 2006-11-13 en_US
dc.description.abstract In this thesis I focus on cutting planes for large Mixed Integer Programming (MIP) problems. More specifically, I focus on two independent cutting planes studies. The first of these deals with cutting planes for the Traveling Salesman Problem (TSP), and the second with cutting planes for general MIPs. In the first study I introduce a new class of cutting planes which I call the Generalized Domino Parity (GDP) inequalities. My main achievements with regard to these are: (1) I show that these are valid for the TSP and for the graphical TSP. (2) I show that they generalize most well-known TSP inequalities (including combs, domino-parity constraints, clique-trees, bipartitions, paths and stars). (3) I show that a sub-class of these (which contains all clique-tree inequalities w/ a fixed number of handles) can be separated in polynomial time, on planar graphs. My second study can be subdivided in two parts. In the first of these I study the Mixed Integer Knapsack Problem (MIKP) and develop a branch-and-bound based algorithm for solving it. The novelty of the approach is that it exploits the notion of "dominance" in order to effectively prune solutions in the branch-and-bound tree. In the second part, I develop a Mixed Integer Rounding (MIR) cut separation heuristic, and embed the MIKP solver in a column generation algorithm in order to assess the performance of said heuristic. The goal of this study is to understand why no other class of inequalities derived from single-row systems has been able to outperform the MIR. Computational results are presented. en_US
dc.description.degree Ph.D. en_US
dc.format.extent 1425451 bytes
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/13956
dc.language.iso en_US
dc.publisher Georgia Institute of Technology en_US
dc.subject Traveling salesman problem en_US
dc.subject Cutting planes en_US
dc.subject Mixed integer rounding en_US
dc.subject Mixed integer programming en_US
dc.title Cutting Planes for Large Mixed Integer Programming Models en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename H. Milton Stewart School of Industrial and Systems Engineering
local.contributor.corporatename College of Engineering
relation.isOrgUnitOfPublication 29ad75f0-242d-49a7-9b3d-0ac88893323c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
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