A New Lower Bound via Projection for the Quadratic Assignment Problem (1992)
| Venue: | Mathematics of Operations Research |
| Citations: | 48 - 16 self |
BibTeX
@ARTICLE{Hadley92anew,
author = {S.W. Hadley and F. Rendl and H. Wolkowicz},
title = {A New Lower Bound via Projection for the Quadratic Assignment Problem},
journal = {Mathematics of Operations Research},
year = {1992},
volume = {17},
pages = {727--739}
}
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Abstract
New lower bounds for the quadratic assignment problem QAP are presented. These bounds are based on the orthogonal relaxation of QAP. The additional improvement is obtained by making efficient use of a tractable representation of orthogonal matrices having constant row and column sums. The new bound is easy to implement and often provides high quality bounds under an acceptable computational effort. Key Words: quadratic assignment problem, lower bounds, relaxations, orthogonal projection, eigenvalue bounds. 0 The authors would like to thank the Natural Sciences and Engineering Research Council of Canada and the Austrian Science Foundatation (FWF) for their support. 1 Introduction The Quadratic Assignment Problem QAP is a generic model for various problems arising e.g. in location theory, VLSI design, facility layout, keyboard design and many other areas, see [1] for a recent survey on the QAP. Formally the QAP consists of minimizing f(X) = tr(AXB t + C)X t over the set of permu...
