Article

Mathematical Programming

, Volume 91, Issue 3, pp 563-588

Solving large quadratic assignment problems on computational grids

  • Kurt AnstreicherAffiliated withDepartment of Management Sciences, University of Iowa, Iowa City, IA 52242, USA, e-mail: kurt-anstreicher@uiowa.edu
  • , Nathan BrixiusAffiliated withDepartment of Computer Science, University of Iowa, Iowa City, IA 52242, USA, e-mail: brixius@cs.uiowa.edu
  • , Jean-Pierre GouxAffiliated withDepartment of Electrical and Computer Engineering, Northwestern University, and Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA, e-mail: goux@ece.nwu.edu
  • , Jeff LinderothAffiliated withMathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439, USA, e-mail: linderot@mcs.anl.gov

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Abstract.

The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms. In this article we describe a novel approach to solve QAPs using a state-of-the-art branch-and-bound algorithm running on a federation of geographically distributed resources known as a computational grid. Solution of QAPs of unprecedented complexity, including the nug30, kra30b, and tho30 instances, is reported.

Key words: Quadratic assignment problem – branch and bound – computational grid – metacomputing Mathematics Subject Classification (1991): 90C27, 90C09, 90C20