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Lower bounds for the quadratic assignment problem
 University of Munich
, 1994
"... Abstract. We investigate the classical GilmoreLawler lower bound for the quadratic assignment problem. We provide evidence of the difficulty of improving the GilmoreLawler Bound and develop new bounds by means of optimal reduction schemes. Computational results are reported indicating that the new ..."
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Cited by 20 (5 self)
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Abstract. We investigate the classical GilmoreLawler lower bound for the quadratic assignment problem. We provide evidence of the difficulty of improving the GilmoreLawler Bound and develop new bounds by means of optimal reduction schemes. Computational results are reported indicating
Solving Large Quadratic Assignment Problems in Parallel.
 Computational Optimization and Applications
, 1994
"... . Quadratic Assignment problems are in practice among the most difficult to solve in the class of NPcomplete problems. The only successful approach hitherto has been BranchandBound based algorithms, but such algorithms are crucially dependent on good bound functions to limit the size of the space ..."
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Cited by 30 (6 self)
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vector processors, and have hence not been ideally suited for computations essentially involving nonvectorizable computations on integers. In this paper we investigate the combination of one of the best bound functions for a Branchand Bound algorithm (the GilmoreLawler bound) and various testing
A HEURISTIC ALGORITH4 FOR THE FACILITIES LAYOUT PROBLEM by
, 1988
"... This paper presents a heuristic algorithm for solving the facilities layout problem. The basic approach is the combination of a constructive method with exchange procedures, used repetitively. The constructive heuristic uses alternate costs, obtained in the process of computing the GilmoreLawler ..."
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This paper presents a heuristic algorithm for solving the facilities layout problem. The basic approach is the combination of a constructive method with exchange procedures, used repetitively. The constructive heuristic uses alternate costs, obtained in the process of computing the GilmoreLawler
A Parallel Computational Framework for Solving Quadratic Assignment Problems Exactly
, 2010
"... The Quadratic Assignment Problem (QAP) is a combinatorial optimization problem used to model a number of different engineering applications. Originally it was the problem of optimally placing electronic components to minimize wire length. However, essentially the same problem occurs in backboard ..."
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the GilmoreLawler bound (GLB). The GLB was computed using a custom implementation of the KuhnMunkres algorithm to solve the associated linear assignment problem (LAP). The core backtracking solver uses the unique approach of only considering partial solutions rather than recursively solving sub
Implementation Of A Variance Reduction Based Lower Bound In A Branch And Bound Algorithm For The Quadratic Assignment Problem
, 1997
"... . The efficient implementation of a branch and bound algorithm for the quadratic assignment problem (QAP), incorporating the lower bound, based on variance reduction, of Li, Pardalos, Ramakrishnan, and Resende (1994), is presented. A new data structure for efficient implementation of branch and boun ..."
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Cited by 5 (1 self)
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and bound algorithms for the QAP is introduced. Computational experiments with the branch and bound algorithm on different classes of QAP test problems are reported. The branch and bound algorithm using the new lower bounds is compared with the same algorithm utilizing the commonly applied GilmoreLawler
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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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