Solving the quadratic assignment problem by means of general purpose mixed integer linear programming solvers
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The Quadratic Assignment Problem (QAP) can be solved by linearization, where one formulates the QAP as a mixed integer linear programming (MILP) problem. On the one hand, most of these linearizations are tight, but rarely exploited within a reasonable computing time because of their size. On the other hand, Kaufman and Broeckx formulation (Eur. J. Oper. Res. 2(3):204–211, 1978) is the smallest of these linearizations, but very weak. In this paper, we analyze how the Kaufman and Broeckx formulation can be tightened to obtain better QAP-MILP formulations. As shown in our numerical experiments, these tightened formulations remain small but computationally effective to solve the QAP by means of general purpose MILP solvers.
KeywordsQuadratic assignment problem Mixed integer linear programming
Thanks are due to the support of the National Natural Science Foundation of China (Grant No. 70871081), and to the support from MAEC-AECID fellowship from the Spanish government. We wish to thank the Faculty of Sciences of the University of Lisbon for providing the software Cplex 11.2. We also thank the support of the grant S2009/esp-1594 from the ‘Comunidad de Madrid’ (Spain) and the grant MTM2009-14039-C06-03 from the Spanish government.
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