The Quadratic Assignment Problem

Abstract

The quadratic assignment problem is reviewed in this chapter. Weights between pairs of facilities and distances between the same number of locations are given. The problem is to find the assignment of facilities to locations that minimizes the weighted sum of distances. This problem is considered to be one of the most difficult combinatorial optimization problems.

A Hybrid Genetic-Hierarchical Algorithm for the Quadratic Assignment Problem

“…The quadratic assignment problem (QAP) [ 1 , 2 , 3 , 4 , 5 , 6 ] is mathematically formulated as follows: Given two non-negative integer matrices , , and the set of all possible permutations of the integers from to , find a permutation that minimizes the following objective function: …”

“…The other important areas of applications of the QAP are as follows: assigning runners in relay teams [ 9 ], clustering [ 10 ], computer/telephone keyboard design [ 11 , 12 , 13 ], planning of airport terminals [ 14 ], facility location [ 15 ], formation of chemical molecular compounds [ 16 ], formation of grey patterns [ 17 ], index assignment [ 18 ], microarray layout [ 19 ], numerical analysis [ 20 ], office assignment and planning of buildings [ 21 , 22 ], seed orchard design [ 23 ], turbine balancing [ 24 ], website structure design [ 25 ]. More examples of the practical applications of the QAP can be found in [ 4 , 26 ].…”

“…Finally, the algorithms inspired from real-world phenomena (including those using metaphors) are also applicable to the QAP [ 90 , 96 , 98 , 110 , 111 , 112 , 113 , 114 , 115 , 116 , 117 , 118 ]. For more extensive surveys and literature reviews on the QAP, the reader is referred to [ 4 , 119 ].…”

Quantum-Inspired Evolutionary Approach for the Quadratic Assignment Problem

“…Intensive studies on quadratic assignment problems produced many algorithms over the last few decades. For a survey on these methods, see [ 3 , 4 ]. It should be mentioned that the performance of the methods for solving the quadratic assignment problems depends on the complexity of the problems.…”

“…Therefore, to obtain near-optimal solutions, various heuristic and metaheuristic approaches have been developed, such as tabu search [ 5 , 6 , 7 ], simulated annealing [ 8 , 9 ], scatter search or swarm algorithms including ant colony optimization [ 10 ], particle swarm optimization [ 11 , 12 ] and bees algorithm [ 13 , 14 ]. One of the initiatives followed by many researchers is using evolutionary algorithms for solving quadratic assignment problems [ 3 , 15 , 16 , 17 , 18 ]. Although these algorithms do not ensure obtaining optimum solutions, they produce good results in a reasonable computation time.…”