A new matrix splitting based relaxation for the quadratic assignment problem

Marko Lange

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Nowadays, the quadratic assignment problem (QAP) is widely considered as one of the hardest of the NP-hard problems. One of the main reasons for this consideration can be found in the enormous difficulty of computing good quality bounds for branch-and-bound algorithms. The practice shows that even with the power of modern computers QAPs of size n>30 are typically recognized as huge computational problems. In this work, we are concerned with the design of a new low-dimensional semidefinite programming relaxation for the computation of lower bounds of the QAP. We discuss ways to improve the bounding program upon its semidefinite relaxation base and give numerical examples to demonstrate its applicability.

Original languageEnglish
Title of host publicationMathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers
PublisherSpringer Verlag
Pages535-549
Number of pages15
Volume9582
ISBN (Print)9783319328584
DOIs
Publication statusPublished - 2016
Externally publishedYes
Event6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 - Berlin, Germany
Duration: 2015 Nov 112015 Nov 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9582
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015
CountryGermany
CityBerlin
Period15/11/1115/11/13

Fingerprint

Matrix Splitting
Quadratic Assignment Problem
Computational complexity
Semidefinite Programming Relaxation
Semidefinite Relaxation
Branch and Bound Algorithm
NP-hard Problems
Lower bound
Numerical Examples
Computing
Demonstrate

Keywords

  • Quadratic assignment problem
  • Relaxation
  • Semidefinite programming

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Lange, M. (2016). A new matrix splitting based relaxation for the quadratic assignment problem. In Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers (Vol. 9582, pp. 535-549). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582). Springer Verlag. https://doi.org/10.1007/978-3-319-32859-1_45

A new matrix splitting based relaxation for the quadratic assignment problem. / Lange, Marko.

Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Vol. 9582 Springer Verlag, 2016. p. 535-549 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lange, M 2016, A new matrix splitting based relaxation for the quadratic assignment problem. in Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. vol. 9582, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9582, Springer Verlag, pp. 535-549, 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, Berlin, Germany, 15/11/11. https://doi.org/10.1007/978-3-319-32859-1_45
Lange M. A new matrix splitting based relaxation for the quadratic assignment problem. In Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Vol. 9582. Springer Verlag. 2016. p. 535-549. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-32859-1_45
Lange, Marko. / A new matrix splitting based relaxation for the quadratic assignment problem. Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers. Vol. 9582 Springer Verlag, 2016. pp. 535-549 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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