Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004. / Includes bibliographical references. / (cont.) algorithm, at one extreme, and complete enumeration, at the other extreme. We derive worst-case approximation guarantees on the solution produced by such an algorithm for matroids. We then define a continuous relaxation of the original problem and show that some of the derived bounds apply with respect to the relaxed problem. We also report on a new bound for independence systems. These bounds extend, and in some cases strengthen, previously known results for standard best-in greedy. / This dissertation consists of two parts. In the first part, we address a class of weakly-coupled multi-commodity network design problems characterized by restrictions on path flows and 'soft' demand requirements. In the second part, we address the abstract problem of maximizing non-decreasing submodular functions over independence systems, which arises in a variety of applications such as combinatorial auctions and facility location. Our objective is to develop approximate solution procedures suitable for large-scale instances that provide a continuum of trade-offs between accuracy and tractability. In Part I, we review the application of Dantzig-Wolfe decomposition to mixed-integer programs. We then define a class of multi-commodity network design problems that are weakly-coupled in the flow variables. We show that this problem is NP-complete, and proceed to develop an approximation/reformulation solution approach based on Dantzig-Wolfe decomposition. We apply the ideas developed to the specific problem of airline fleet assignment with the goal of creating models that incorporate more realistic revenue functions. This yields a new formulation of the problem with a provably stronger linear programming relaxation, and we provide some empirical evidence that it performs better than other models proposed in the literature. In Part II, we investigate the performance of a family of greedy-type algorithms to the problem of maximizing submodular functions over independence systems. Building on pioneering work by Conforti, Cornu6jols, Fisher, Jenkyns, Nemhauser, Wolsey and others, we analyze a greedy algorithm that incrementally augments the current solution by adding subsets of arbitrary variable cardinality. This generalizes the standard best-in greedy / by Amr Farahat. / Ph.D.
| Identifer | oai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/28857 |
| Date | January 2004 |
| Creators | Farahat, Amr, 1973- |
| Contributors | Cynthia Barnhart., Massachusetts Institute of Technology. Operations Research Center., Massachusetts Institute of Technology. Operations Research Center. |
| Publisher | Massachusetts Institute of Technology |
| Source Sets | M.I.T. Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Format | 141 p., 5774849 bytes, 5793335 bytes, application/pdf, application/pdf, application/pdf |
| Rights | M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission., http://dspace.mit.edu/handle/1721.1/7582 |
Page generated in 0.0017 seconds