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Semidefinite Programming Approaches to the Quadratic Assignment Problem

  • Henry Wolkowicz
Part of the Combinatorial Optimization book series (COOP, volume 7)

Abstract

The Quadratic Assignment Problem, QAP, is arguably the hardest of the NP-hard problems. One of the main reasons is that it is very difficult to get good quality bounds for branch and bound algorithms. We show that many of the bounds that have appeared in the literature can be ranked and put into a unified Semidefinite Programming, SDP, framework. This is done using redundant quadratic constraints and Lagrangian relaxation. Thus, the final SDP relaxation ends up being the strongest.

Keywords

Assignment Problem Positive Semidefinite Lagrangian Relaxation Strong Duality Quadratic Assignment Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Henry Wolkowicz
    • 1
  1. 1.Department of Combinatorics and Optimization WaterlooCanada

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