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      • Theses - Department of Industrial Engineering
      • Dept. of Industrial Engineering - Ph.D. / Sc.D.
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      Quadratic assignment problem : linearizations and polynomial time solvable cases

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      Author
      Erdoğan, Güneş
      Advisor
      Tansel, Barbaros Ç.
      Date
      2006
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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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 Problem
      Linearization
      Computational Complexity
      Polynomial Time Solvability
      Permalink
      http://hdl.handle.net/11693/29917
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      • Dept. of Industrial Engineering - Ph.D. / Sc.D. 46
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