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Effective formulation reductions for the quadratic assignment problem

Huizhen Zhang(zhzzywz***at***gmail.com)
Cesar Beltran-Royo(cesar.beltran***at***urjc.es)
Miguel Constantino(miguel.constantino***at***fc.ul.pt)

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, which we call formulation IPQAP-I. 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 32 QAPLIB instances, which range from 12 to 32 locations, are presented. The proposed reductions turned out to be very effective: By applying the new constraint reduction or the new variable reduction to the IPQAP-I formulation, we solved 13 and 23 instances, respectively, compared to the 7 instances solved by formulation IPQAP-I.

Keywords: quadratic assignment problem, linear integer programming, linear programming relaxation, sparse matrix

Category 1: Combinatorial Optimization

Citation:

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Entry Submitted: 12/17/2008
Entry Accepted: 12/17/2008
Entry Last Modified: 12/17/2008

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