RETRACTED ARTICLE: A comprehensive review of quadratic assignment problem: variants, hybrids and applications

Abdel‐Basset, Mohamed; Manogaran, Gunasekaran; Rashad, Heba; Zaied, Abdel Nasser H.

doi:10.1007/s12652-018-0917-x

Cited by 42 publications

(20 citation statements)

References 176 publications

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“…Fixing an open [i, r] (say, [5,1]), leads to a unimodular structure saying that there must exist positive values of connectedness to each of the other levels and stages (excluding level 5 and stage 1). Having w [5,1] > 0 can be thought of as representing a colored (say, grey) "thread," "rooted" in node [5,1] which needs to be "weaved" through the graph to cover every level and every stage. Of course, at this point we will have multiple colored threads rooted in our open [i, r] nodes corresponding to each positive w [i,r] .…”

Section: Visualization Of the Model Structurementioning

confidence: 99%

“…That is, open nodes "span" the levels and stages of the graph in pairs, for a third node with which to have connectedness. Hence, the constraints can be thought of as saying that every color of thread must have the same "color intensity" (shade of grey, in the case of [5,1]) at all stages and all levels of the assignment graph, respectively. Now, we can say that the threads are 'balanced' across all levels and stages so that each colored thread must correspond to a TSP path.…”

Section: Visualization Of the Model Structurementioning

confidence: 99%

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Exact extended formulation of the linear assignment problem (LAP) polytope for solving the traveling salesman and quadratic assignment problems

Diaby

Karwan

Sun

2016

Preprint

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We present an O(n 6 ) linear programming model for the traveling salesman (TSP) and quadratic assignment (QAP) problems. The basic model is developed within the framework of the TSP. It does not involve the city-to-city variables-based, traditional TSP polytope referred to in the literature as "the TSP polytope." We do not model explicit Hamiltonian cycles of the cities. Instead, we use a time-dependent abstraction of TSP tours and develop a direct extended formulation of the linear assignment problem (LAP) polytope. The model is exact in the sense that it has integral extreme points which are in one-to-one correspondence with TSP tours. It can be solved optimally using any linear programming (LP) solver, hence offering a new (incidental) proof of the equality of the computational complexity classes "P " and "N P ." The extensions of the model to the time-dependent traveling salesman problem (TDTSP) as well as the quadratic assignment problem (QAP) are straightforward. The reasons for the non-applicability of existing negative extended formulations results for "the TSP polytope" to the model in this paper as well as our software implementation and the computational experimentation we conducted are briefly discussed.

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Section: Visualization Of the Model Structurementioning

confidence: 99%

Section: Visualization Of the Model Structurementioning

confidence: 99%

Exact extended formulation of the linear assignment problem (LAP) polytope for solving the traveling salesman and quadratic assignment problems

Diaby

Karwan

Sun

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…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 ].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Genetic-Hierarchical Algorithm for the Quadratic Assignment Problem

Misevičius

Verenė

2021

Entropy

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In this paper, we present a hybrid genetic-hierarchical algorithm for the solution of the quadratic assignment problem. The main distinguishing aspect of the proposed algorithm is that this is an innovative hybrid genetic algorithm with the original, hierarchical architecture. In particular, the genetic algorithm is combined with the so-called hierarchical (self-similar) iterated tabu search algorithm, which serves as a powerful local optimizer (local improvement algorithm) of the offspring solutions produced by the crossover operator of the genetic algorithm. The results of the conducted computational experiments demonstrate the promising performance and competitiveness of the proposed algorithm.

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“…The QAP is regarded as a problem of NP-Hard combinatorial optimization (Şahinkoç & Bilge, 2018), which serves as a model for many real-life applications such as hospital layout, backboard wiring, campus layout, scheduling and designing of keyboard typewriter, etc. ever since the QAP was formulated, the attention of researchers has been drawn to it because of its importance in theory and practice, and most importantly because of how complex it is (Duman et al, 2012;Benlic & Hao, 2013;Abdel-Basset et al, 2018a, Cela et al, 2018. The FLP has been introduced as a QAP in order to identify the ideal allocation of N facilities to N locations, where there must be equality between the number of locations and number of facilities.…”

Section: Introductionmentioning

confidence: 99%

A new hybrid approach based on discrete differential evolution algorithm to enhancement solutions of quadratic assignment problem

Hameed¹,

Aboobaider²,

Mutar³

et al. 2020

10.5267/j.ijiec

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The Combinatorial Optimization Problem (COPs) is one of the branches of applied mathematics and computer sciences, which is accompanied by many problems such as Facility Layout Problem (FLP), Vehicle Routing Problem (VRP), etc. Even though the use of several mathematical formulations is employed for FLP, Quadratic Assignment Problem (QAP) is one of the most commonly used. One of the major problems of Combinatorial NP-hard Optimization Problem is QAP mathematical model. Consequently, many approaches have been introduced to solve this problem, and these approaches are classified as Approximate and Exact methods. With QAP, each facility is allocated to just one location, thereby reducing cost in terms of aggregate distances weighted by flow values. The primary aim of this study is to propose a hybrid approach which combines Discrete Differential Evolution (DDE) algorithm and Tabu Search (TS) algorithm to enhance solutions of QAP model, to reduce the distances between the locations by finding the best distribution of N facilities to N locations, and to implement hybrid approach based on discrete differential evolution (HDDETS) on many instances of QAP from the benchmark. The performance of the proposed approach has been tested on several sets of instances from the data set of QAP and the results obtained have shown the effective performance of the proposed algorithm in improving several solutions of QAP in reasonable time. Afterwards, the proposed approach is compared with other recent methods in the literature review. Based on the computation results, the proposed hybrid approach outperforms the other methods.

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RETRACTED ARTICLE: A comprehensive review of quadratic assignment problem: variants, hybrids and applications

Cited by 42 publications

References 176 publications

Exact extended formulation of the linear assignment problem (LAP) polytope for solving the traveling salesman and quadratic assignment problems

Exact extended formulation of the linear assignment problem (LAP) polytope for solving the traveling salesman and quadratic assignment problems

A Hybrid Genetic-Hierarchical Algorithm for the Quadratic Assignment Problem

A new hybrid approach based on discrete differential evolution algorithm to enhancement solutions of quadratic assignment problem

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