scholarly journals New special cases of the Quadratic Assignment Problem with diagonally structured coefficient matrices

2018 ◽  
Vol 267 (3) ◽  
pp. 818-834 ◽  
Author(s):  
Eranda Çela ◽  
Vladimir Deineko ◽  
Gerhard J. Woeginger
Keyword(s):  
Assignment Problem ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment ◽  
Special Cases

The Rank-One Quadratic Assignment Problem

2020 ◽  
Author(s):  
Yang Wang ◽  
Wei Yang ◽  
Abraham P. Punnen ◽  
Jingbo Tian ◽  
Aihua Yin ◽  
...  
Keyword(s):  
Integer Programming ◽  
Assignment Problem ◽  
Computational Study ◽  
Quadratic Assignment Problem ◽  
Research Work ◽  
Programming Models ◽  
Quadratic Assignment ◽  
Computational Results ◽  
Special Cases ◽  
Rank One

In this paper, we study the quadratic assignment problem with a rank-one cost matrix (QAP-R1). Four integer-programming formulations are introduced of which three are assumed to have partial integer data. Unlike the standard quadratic assignment problem, some of our formulations can solve reasonably large instances of QAP-R1 with impressive running times and are faster than some metaheuristics. Pairwise relative strength of the LP relaxations of these formulations are also analyzed from theoretical and experimental points of view. Finally, we present a new metaheuristic algorithm to solve QAP-R1 along with its computational analysis. Our study offers the first systematic experimental analysis of integer-programming models and heuristics for QAP-R1. The benchmark instances with various characteristics generated for our study are made available to the public for future research work. Some new polynomially solvable special cases are also introduced. Summary of Contribution: This paper aims to advance our knowledge and ability in solving an important special case of the quadratic assignment problem. It shows how to exploit inherent properties of an optimization problem to achieve computational advantages, a strategy that was followed by researchers in model building and algorithm developments for decades. Our computational results attest to this time-tested general philosophy. The paper presents the first systematic computational study of the rank one quadratic assignment problem, along with new mathematical programming models and complexity analysis. We believe the theoretical and computational results of this paper will inspire further research on the topic and will be of significant value to practitioners using rank one quadratic assignment models.

The Quadratic Assignment Problem

1963 ◽  
Vol 9 (4) ◽  
pp. 586-599 ◽  
Author(s):  
Eugene L. Lawler
Keyword(s):  
Assignment Problem ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment

A Memetic Heuristic for the Generalized Quadratic Assignment Problem

2006 ◽  
Vol 18 (4) ◽  
pp. 433-443 ◽  
Author(s):  
Jean-François Cordeau ◽  
Manlio Gaudioso ◽  
Gilbert Laporte ◽  
Luigi Moccia
Keyword(s):  
Assignment Problem ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment ◽  
Generalized Quadratic Assignment Problem
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