1. Institut für Mathematik, Universit?t Klagenfurt, Universit?tsstra?e 65-67, 9020, Klagenfurt, Austria 2. Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, 3010, Australia
Abstract:
Semidefinite programming (SDP) has recently turned out to be a very powerful tool for approximating some NP-hard problems.
The nature of the quadratic assignment problem (QAP) suggests SDP as a way to derive tractable relaxations. We recall some
SDP relaxations of QAP and solve them approximately using a dynamic version of the bundle method. The computational results
demonstrate the efficiency of the approach. Our bounds are currently among the strongest ones available for QAP. We investigate
their potential for branch and bound settings by looking also at the bounds in the first levels of the branching tree.