Mathematical Programming

, Volume 89, Issue 3, pp 341-357

A new bound for the quadratic assignment problem based on convex quadratic programming

  • Kurt M. AnstreicherAffiliated withDepartment of Management Sciences, University of Iowa, Iowa City, IA 52242, e-mail: kurt-anstreicher@uiowa.edu
  • , Nathan W. BrixiusAffiliated withDepartment of Computer Science, University of Iowa, Iowa City, IA 52242, e-mail: brixius@cs.uiowa.edu

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Abstract.

We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the well-known projected eigenvalue bound, and appears to be competitive with existing bounds in the trade-off between bound quality and computational effort.

Key words: quadratic assignment problem – eigenvalue bounds – quadratic programming – semidefinite programming
Mathematics Subject Classification (1991): 90C27, 90C09, 90C20