A Dual Framework for Lower Bounds of the Quadratic Assignment Problem Based on Linearization

Computing ◽  
1999 ◽  
Vol 63 (4) ◽  
pp. 351-403 ◽  
Author(s):  
S. E. Karisch ◽  
E. Çela ◽  
J. Clausen ◽  
T. Espersen
Keyword(s):  
Lower Bounds ◽  
Assignment Problem ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment

Lower bounds for the quadratic assignment problem

1994 ◽  
Vol 50 (1) ◽  
pp. 387-410 ◽  
Author(s):  
Y. Li ◽  
P. M. Pardalos ◽  
K. G. Ramakrishnan ◽  
M. G. C. Resende
Keyword(s):  
Lower Bounds ◽  
Assignment Problem ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment

scholarly journals How to start a heuristic? Utilizing lower bounds for solving the quadratic assignment problem

2022 ◽  
Vol 13 (2) ◽  
pp. 151-164 ◽  
Author(s):  
Radomil Matousek ◽  
Ladislav Dobrovsky ◽  
Jakub Kudela
Keyword(s):  
Lower Bounds ◽  
Assignment Problem ◽  
Optimization Problems ◽  
Quadratic Assignment Problem ◽  
Computation Time ◽  
Quadratic Assignment ◽  
Combinatorial Optimization Problems ◽  
Lower Bounding ◽  
Programming Techniques

The Quadratic Assignment Problem (QAP) is one of the classical combinatorial optimization problems and is known for its diverse applications. The QAP is an NP-hard optimization problem which attracts the use of heuristic or metaheuristic algorithms that can find quality solutions in an acceptable computation time. On the other hand, there is quite a broad spectrum of mathematical programming techniques that were developed for finding the lower bounds for the QAP. This paper presents a fusion of the two approaches whereby the solutions from the computations of the lower bounds are used as the starting points for a metaheuristic, called HC12, which is implemented on a GPU CUDA platform. We perform extensive computational experiments that demonstrate that the use of these lower bounding techniques for the construction of the starting points has a significant impact on the quality of the resulting solutions.

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