Bounds for the quadratic assignment problem using the bundle method

Authors:
Franz Rendl;Renata Sotirov
Affiliations:
Universität Klagenfurt, Institut für Mathematik, Universitätsstraße 65-67, 9020, Klagenfurt, Austria;The University of Melbourne, Department of Mathematics and Statistics, Universitätsstraße 65-67, 3010, Parkville, VIC, Australia
Venue:
Mathematical Programming: Series A and B
Year:
2007

Citing 0
Cited 7

An algorithm for the generalized quadratic assignment problem

Computational Optimization and Applications
A Low-Dimensional Semidefinite Relaxation for the Quadratic Assignment Problem

Mathematics of Operations Research
Semidefinite approximations for quadratic programs over orthogonal matrices

Journal of Global Optimization
An iterative scheme for valid polynomial inequality generation in binary polynomial programming

IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Estimating Bounds for Quadratic Assignment Problems Associated with Hamming and Manhattan Distance Matrices Based on Semidefinite Programming

SIAM Journal on Optimization
A Level-3 Reformulation-Linearization Technique-Based Bound for the Quadratic Assignment Problem

INFORMS Journal on Computing
Copositive and semidefinite relaxations of the quadratic assignment problem

Discrete Optimization

Quantified Score

Hi-index	0.00

Visualization

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.