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A BranchandBound Algorithm for the Quadratic Assignment Problem Based on the Hungarian Method
 European Journal of Operational Research
, 1996
"... This paper presents a new branchandbound algorithm for solving the Quadratic Assignment Problem (QAP). The algorithm is based on a Dual Procedure (DP) similar to the Hungarian method for solving the Linear Assignment Problem. Our DP solves the QAP in certain cases, i.e., for some small problems (N ..."
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This paper presents a new branchandbound algorithm for solving the Quadratic Assignment Problem (QAP). The algorithm is based on a Dual Procedure (DP) similar to the Hungarian method for solving the Linear Assignment Problem. Our DP solves the QAP in certain cases, i.e., for some small problems (N<7) and for numerous larger problems (7N16) that arise as subproblems of a larger QAP such as the Nugent 20. The DP, however, does not guarantee a solution. It is used in our algorithm to calculate lower bounds on solutions to the QAP. As a result of a number of recently developed improvements, the DP produces lower bounds that are as tight as any which might be useful in a branchandbound algorithm. These are produced relatively cheaply, especially on larger problems. Experimental results show that the computational complexity of our algorithm is lower than known methods, and that its actual runtime is significantly shorter than the best known algorithms for QAPLIB test instances of size 16 through 22. Our method has the potential for being improved and therefore can be expected to aid in solving even larger problems. Keywords Quadratic Assignment Problem, Branchandbound, Quadratic Programming, Integer Programming, Mathematical Programming. 2 1.
A Branch and Bound Algorithm for the Quadratic Assignment Problem using a Lower Bound Based on Linear Programming
 In C. Floudas and P.M. Pardalos, editors, State of the Art in Global Optimization: Computational Methods and Applications
, 1995
"... In this paper, we study a branch and bound algorithm for the quadratic assignment problem (QAP) that uses a lower bound based on the linear programming (LP) relaxation of a classical integer programming formulation of the QAP. Computational experience with the branch and bound algorithm on several Q ..."
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Cited by 10 (2 self)
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In this paper, we study a branch and bound algorithm for the quadratic assignment problem (QAP) that uses a lower bound based on the linear programming (LP) relaxation of a classical integer programming formulation of the QAP. Computational experience with the branch and bound algorithm on several QAP test problems is reported. The linear programming relaxations are solved with an implementation of an interior point algorithm that uses a preconditioned conjugate gradient algorithm to compute directions. The branch and bound algorithm is compared with a similar branch and bound algorithm that uses the GilmoreLawler lower bound (GLB) instead of the LPbased bound. The LPbased algorithm examines a small portion of the nodes explored by the GLBbased algorithm. 1 Introduction The quadratic assignment problem (QAP), first proposed by Koopmans and Beckmann [16], can be stated as min p2\Pi n X i=1 n X j=1 a ij b p(i)p(j) ; To appear in Proceedings of State of the Art in Global Opti...
GRASP: Basic components and enhancements
 Telecommunication Systems
, 2011
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"... ris ptim etw tax bet t sc tera NPhard problems are difficult to solve and no polynomial time. Unfortunately, most combih as the Travelling Salesman, k, Grap red to sually ion an s such ..."
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ris ptim etw tax bet t sc tera NPhard problems are difficult to solve and no polynomial time. Unfortunately, most combih as the Travelling Salesman, k, Grap red to sually ion an s such