Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 1,583 papers for “Quadratic assignment problem”

Quadratic Assignment Problem

Masoumeh Bayat, Mahdieh Sedghi · Contributions to management science · 2009

The quadratic assignment problem (QAP) in location Theory is the problem of locating facilities the cost of placing a facility depends on the distances from other facilities and also the interaction with other facilities. QAP was introduced by Koopmans and Beckman in 1957 who were trying to model a facilities location problem. It is possible to formulate some classic problems of combinatorial optimization, such as the traveling salesman, maximum clique and graph partitioning problems as a QAP. The QAP belongs to the class of NP-complete problems and is considered one of the most difficult combinatorial optimization problems. Exact solution strategies for the QAP have been unsuccessful for large problem (approximately N ≤ 25).

Cited by 7

Quadratic assignment problem

Augusto, Edma Tarine Macedo · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2016

O Problema de Afetação Quadrática, Quadratic Assignment Problem (QAP) tem recebido a atenção da comunidade académica devido a sua importância e complexidade. Este é um dos problemas mais difíceis de otimização combinatória. É fácil de descrever, não é tão fácil de formular e é muito difícil de resolver. O QAP foi introduzido por Koopmans e Beckman em 1957, num contexto económico. A preocupação destes autores era afetar estabelecimentos industriais em locais predeterminados, de tal maneira que o custo de transporte fosse minimizado. Na sua aplicação, o custo é o produto dos termos da matriz fluxo e da matriz distância. Desde o surgimento do QAP uma miríade de aplicações tem emergido. Algumas formulações do QAP apresentadas na literatura foram usadas para resolver o problema com base na atividade de picking. A atividade de picking normalmente representa cerca 50% dos custos de trabalho direto num armazém. Esta atividade despende 50% do seu tempo total em deslocações. Na operação de um armazém de picking, a tomada de decisão quanto à localização dos produtos pode condicionar os custos de deslocação entre as posições dos produtos. Daí a pertinência de modelar o QAP na operação de um armazém de picking. Para tal, inicialmente gerou-se instâncias com dados aleatórios numa aplicação programada em linguagem VBA (Visual Basic Application). De seguida, modelou-se em linguagem AMPL (A Mathematical Programming Language), algumas formulações apresentadas na literatura, designadas por: linearização de Lawler, linearização de Frieze e Yadegar e a linearização de Adam e Johnson. Para serem submetidas no servidor NEOS server (Network-Enabled Optimization System), com as instâncias geradas. As instâncias também foram submetidas no LPSolve e na aplicação da heurística de pesquisa local. Gerou-se uma heurística de pesquisa local em linguagem VBA tendo como suporte o Microsoft Excel. O servidor NEOS server apresentou resultados para instâncias de dimensão até =31. O LPSolve não consegue resolver instâncias de grandes dimensões em tempo computacional aceitável devido ao grande número de variáveis e restrições, uma vez que o LPSolve só resolve problemas com formulação linear inteira mista. A heurística de pesquisa local programada em linguagem VBA obteve resultados em todas instâncias geradas para o propósito deste trabalho.

Cited by 0

The Quadratic Assignment Problem

Eugene L. Lawler · Management Science · 1963

This paper presents a formulation of the quadratic assignment problem, of which the Koopmans-Beckmann formulation is a special case. Various applications for the formulation are discussed. The equivalence of the problem to a linear assignment problem with certain additional constraints is demonstrated. A method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions. Further generalizations to cubic, quartic, N-adic problems are considered.

Cited by 967

LINEARIZING QUADRATIC ASSIGNMENT PROBLEM

Continuous Optimization, Knowledge-based Technologies, L. Sakalauskas et al. · 2015

Abstract: In past several linearization of the Quadratic Assignment Problem (QAP) which is a NP-hard problem have been given (See Lawler (1962) and Christofides et al. (1980)). Here, a new set of con-straints that perfectly linearize the QAP is proposed. The new linearization is compared with other lin-earization and it is found that proposed linearization performs better in time complexity. We have also shown that linear programming relaxations of these linearizations give optimal solution for the 0-1 integer linearization of QAP. Empirical evidence shows that this results in substantial savings in computational time. T-test has been also carried out to show the significance statistically.

Cited by 0

The generalized quadratic assignment problem

Ma Zhong · TSpace · 2003

We study a generalization of the quadratic assignment problem (QAP) by allowing multiple equipments to be assigned at a single location as long as resources at the location permit. This problem arises in many real world applications such as facility location problem and logistics network design. We call the problem as the generalized quadratic assignment problem (GQAP) and show that this relaxation increases the complexity of the problem dramatically. We propose three linearization approaches and a branch and bound algorithm to optimally solve the GQAP. Computational studies have been conducted to demonstrate the performance of the proposed approaches.

Cited by 0Open access

Quadratic Assignment Problem. 1 Acknowledgments

Chris Kerr, To Dr, Irwin Reichstein et al. · 2004

When they introduced the Ant System paradigm, Dorigo, Maniezzo, and Colorni also suggested an improvement to the original algorithm. By making use of global information, a set of ‘elitist ’ ants could focus the search, potentially accelerating convergence on an optimal solution. In a later paper, White, Kaegi, and Oda proposed a refinement of elitism in which local information is used instead of global information. By focusing the search on the local best tours (LBT) rather than the global best tour, the ants could search a wider area and avoid becoming trapped in local optima. Test results using the symmetric Travelling Salesman Problem showed considerable promise. We will examine the effectiveness of this refinement when applied against the assymetrical

Cited by 0

Hybrid metaheuristics for solving the quadratic assignment problem and the generalized quadratic assignment problem

Aldy Gunawan, Kien Ming Ng, Kim Leng Poh et al. · 2014

This paper presents a hybrid metaheuristic for solving the Quadratic Assignment Problem (QAP). The proposed algorithm involves using the Greedy Randomized Adaptive Search Procedure (GRASP) to construct an initial solution, and then using a hybrid Simulated Annealing and Tabu Search (SA-TS) algorithm to further improve the solution. Experimental results show that the hybrid metaheuristic is able to obtain good quality solutions for QAPLIB test problems within reasonable computation time. The proposed algorithm is extended to solve the Generalized Quadratic Assignment Problem (GQAP), with an emphasis on modelling and solving a practical problem, namely an examination timetabling problem. We found that the proposed algorithm is able to perform better than the standard SA algorithm does.

Cited by 8