Quadratic assignment problem : linearizations and polynomial time solvable cases

Date
2006
Instructor
Source Title
Print ISSN
Electronic ISSN
Publisher
Bilkent University
Volume
Issue
Pages
Language
English
Type
Thesis
Journal Title
Journal ISSN
Volume Title
Abstract

The Quadratic Assignment Problem (QAP) is one of the hardest combinatorial optimization problems known. Exact solution attempts proposed for instances of size larger than 15 have been generally unsuccessful even though successful implementations have been reported on some test problems from the QAPLIB up to size 36. In this dissertation, we analyze the binary structure of the QAP and present new IP formulations. We focus on “flow-based” formulations, strengthen the formulations with valid inequalities, and report computational experience with a branch-and-cut algorithm. Next, we present new classes of instances of the QAP that can be completely or partially reduced to the Linear Assignment Problem and give procedures to check whether or not an instance is an element of one of these classes. We also identify classes of instances of the Koopmans-Beckmann form of the QAP that are solvable in polynomial time. Lastly, we present a strong lower bound based on Bender’s decomposition.

Course
Other identifiers
Book Title
Keywords
Quadratic Assignment Problem, Linearization, Computational Complexity, Polynomial Time Solvability
Citation
Published Version (Please cite this version)