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Journal of Combinatorial Optimization

, Volume 30, Issue 3, pp 647–667 | Cite as

On improving convex quadratic programming relaxation for the quadratic assignment problem

  • Yong Xia
  • Wajeb Gharibi
Article
  • 225 Downloads

Abstract

Relaxation techniques play a great role in solving the quadratic assignment problem, among which the convex quadratic programming bound (QPB) is competitive with existing bounds in the trade-off between cost and quality. In this article, we propose two new lower bounds based on QPB. The first dominates QPB at a high computational cost, which is shown equivalent to the recent second-order cone programming bound. The second is strictly tighter than QPB in most cases, while it is solved as easily as QPB.

Keywords

Quadratic assignment problem Lower bound  Capacitated transportation problem Quadratic programming 

Mathematics Subject Classification

90C10 90C20 90C26 

Notes

Acknowledgments

The authors are grateful to the two anonymous referees for their valuable comments and suggestions that have greatly helped the authors improve the paper. This research was supported by National Natural Science Foundation of China under grants 11001006 and 91130019/A011702, by the fund of State Key Laboratory of Software Development Environment under grant SKLSDE-2013ZX-13.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Software Development Environment, LMIB of the Ministry of Education, School of Mathematics and System SciencesBeihang UniversityBeijing People’s Republic of China
  2. 2.College of Computer Science and Information SystemsJazan UniversityJazan Kingdom of Saudhi Arabia

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