A multiscale approximation algorithm for the cardinality constrained knapsack problem

I develop a multiscale approximation algorithm for the cardinality constrained knapsack problem. The algorithm consists of three steps: a rounding and reduction step where a hierarchical representation of the problem data ranging from coarse to fine is generated, a solution step where a coarse solution is computed, and a refinement step where the accuracy of the solution is improved by refining the problem representation. I demonstrate that the algorithm is fully polynomial with a runtime complexity that improves upon the previous best known fully polynomial approximation scheme. Through an extensive computational study, I show that the running times of the algorithm is less than or equal to that of a commercial integer programming package with little loss in solution accuracy.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Civil and Environmental Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Krishnan, Bharath Kumar

Advisor dc:contributor.advisor

• George A. Kocur.

• Civil and Environmental Engineering.

Statement dc: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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34612

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34612