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 suggests SDP as a way to derive tractable relaxation. We recall some SDP relaxations of QAP and solve them approximately using the Bundle Method. The computational results demonstrate the efficiency of the approach. Our bounds are the currently 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.
Citation
unpublished: report, University of Klagenfurt, Universitaetsstrasse 65-67, Austria 2003