Quadratic assignment problem : linearizations and polynomial time solvable cases
Author
Erdoğan, Güneş
Advisor
Tansel, Barbaros Ç.
Date
2006Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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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.
Keywords
Quadratic Assignment ProblemLinearization
Computational Complexity
Polynomial Time Solvability