A multiscale approximation algorithm for the cardinality constrained knapsack problem

• Main Author: Krishnan, Bharath Kumar
• Other Authors: George A. Kocur.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2006
• Subjects: Civil and Environmental Engineering.
• Online Access: http://hdl.handle.net/1721.1/34612

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2006. === Includes bibliographical references (leaves 83-86). === 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. === by Bharath Kumar Krishnan. === Ph.D.