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SOLVING QUADRATIC ASSIGNMENT
PROBLEMS USING CONVEX QUADRATIC
PROGRAMMING RELAXATIONS
Nathan W. Brixius
Dept. of Computer Science, University of Iowa, Iowa City, IA 52242
Kurt M. Anstreicher
Dept. of Management Sciences, University of Iowa, Iowa City, IA 52242
We describe a branchandbound algorithm for the quadratic assignment problem (QAP) that
uses a convex quadratic programming (QP) relaxation to obtain a bound at each node. The
QP subproblems are approximately solved using the FrankWolfe algorithm, which in this case
requires the solution of a linear assignment problem on each iteration. Our branching strategy
makes extensive use of dual information associated with the QP subproblems. We obtain state
oftheart computational results on large benchmark QAPs.
KEY WORDS: Quadratic assignment problem, branchandbound, quadratic programming,
FrankWolfe algorithm
1 INTRODUCTION
The quadratic assignment problem (QAP) in \KoopmansBeckmann" form is
QAP(A B C) : min tr(AXB +C)XT
s:t: X 2
