scholarly journals Quadratic Assignment Problem and its Relevance to the Real World: A Survey

2014 ◽  
Vol 96 (9) ◽  
pp. 42-47
Author(s):  
Ravi KumarBhati ◽  
Akhtar Rasool
2021 ◽  
Vol 20 (9) ◽  
Author(s):  
Carlos D. Gonzalez Calaza ◽  
Dennis Willsch ◽  
Kristel Michielsen

AbstractWe benchmark the 5000+ qubit system coupled with the Hybrid Solver Service 2 released by D-Wave Systems Inc. in September 2020 by using a new class of optimization problems called garden optimization problems known in companion planting. These problems are scalable to an arbitrarily large number of variables and intuitively find application in real-world scenarios. We derive their QUBO formulation and illustrate their relation to the quadratic assignment problem. We demonstrate that the system and the new hybrid solver can solve larger problems in less time than their predecessors. However, we also show that the solvers based on the 2000+ qubit system sometimes produce more favourable results if they can solve the problems.


2014 ◽  
pp. 139-148
Author(s):  
Alexander Kolomiychuk

This paper presents the analysis of the 2-sum problem and the spectral algorithm. The spectral algorithm was proposed by Barnard, Pothen and Simon in [1]; its heuristic properties have been advocated by George and Pothen in [4] by formulation of the 2-sum problem as a Quadratic Assignment Problem. In contrast to that analysis another approach is proposed: permutations are considered as vectors of Euclidian space. This approach enables one to prove the bound results originally obtained in [4] in an easier way. The geometry of permutations is considered in order to explain what are ‘good’ and ‘pathological’ situations for the spectral algorithm. Upper bounds for approximate solutions generated by the spectral algorithm are proved. The results of numerical computations on (graphs of) large sparse matrices from real-world applications are presented to support the obtained results and illustrate considerations related to the ‘pathological’ cases.


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

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