Effective formulation reductions for the quadratic assignment problem

Authors:
Huizhen Zhang;Cesar Beltran-Royo;Miguel Constantino
Affiliations:
Statistics and Operations Research, Rey Juan Carlos University, Madrid, Spain;Statistics and Operations Research, Rey Juan Carlos University, Madrid, Spain;DEIO/Centro de Investigação Operacional, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal
Venue:
Computers and Operations Research
Year:
2010

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Abstract

In this paper we study two formulation reductions for the quadratic assignment problem (QAP). In particular we apply these reductions to the well known Adams and Johnson [2] integer linear programming formulation of the QAP. We analyze two cases: In the first case, we study the effect of constraint reduction. In the second case, we study the effect of variable reduction in the case of a sparse cost matrix. Computational experiments with a set of 30 QAPLIB instances, which range from 12 to 32 locations, are presented. The proposed reductions turned out to be very effective.