On the quadratic assignment problem

Frieze, Alan; Yadegar, Jacob

doi:10.1016/0166-218x(83)90018-5

Cited by 115 publications

(69 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Several authors proposed different approaches to improve the GLB, Frieze and Yadegar (1983) proposed GLB with decomposition, Assad and Xu (1985) proposed the AX bound that is obtained iteratively, where n 2 C 1 assignment of size n are solved in each iteration. Hence, the running time to compute is O.k n 5 / where k is the number of iterations.…”

Section: The Gilmore and Lawler Lower Bound (Glb)mentioning

confidence: 99%

Demand Point Aggregation Analaysis for Location Models

Sadigh

Fallah

2009

Facility Location

View full text Add to dashboard Cite

Section: The Gilmore and Lawler Lower Bound (Glb)mentioning

confidence: 99%

Demand Point Aggregation Analaysis for Location Models

Sadigh

Fallah

2009

Facility Location

View full text Add to dashboard Cite

“…There exist several lower-bounding procedures such as those of Gilmore [lo] [ 6 ] , Christofides, Mingozzi, and Toth [ 5 ] , and Frieze and Yadegar [ 8 ] . Considering the strength of the bounds and the computational effort, the procedure of Gilmore-Lawler seems to be the most effective.…”

Section: An Exact Branch-and-bound Proceduresmentioning

confidence: 99%

A branch‐and‐bound‐based heuristic for solving the quadratic assignment problem

Bazaraa¹,

Kirca

1983

Naval Research Logistics

View full text Add to dashboard Cite

In this article a branch-and-bound algorithm is proposed for solving the quadratic assignment problem. Using symmetric properties of the problem, the algorithm eliminates "mirror image" branches, thus reducing the search effort. Several routines that transform the procedure into an efficient heuristic are also implemented. These include certain 2-way and 4-way exchanges, selective branching rules, and the use of variable upperbounding techniques for enhancing the speed of fathoming. The computational results are quite encouraging. As an exact scheme, the algorithm solved the 12-facility problem of Nugent et al. and the 19-facility problem of Elshafei. More importantly, as a heuristic, the procedure produced the best known solutions for all well-known problems in the literature, and produced improved solutions in several cases.

show abstract

“…(1) Formulações por Programação Inteira são dadas por programação binária, como a de [KB57], ou por Programação Mista, como as de [KB78], [FY83] e [PR96]. Nesta linha, diversos limites inferiores do tipo linear foram determinados, inclusive um dos mais antigos deles, conhecido por limite de Gilmore e Lawler e suas variações, [Gi62] e [La63];…”

Section: Introductionunclassified

Ordenações parciais nos conjuntos das soluções dos problemas de alocação linear e quadrático

Rangel

Abreu

2003

Pesqui. Oper.

View full text Add to dashboard Cite

ResumoO Problema Quadrático de Alocação, PQA, pode ser abordado através de uma relaxação na forma do Problema de Alocação Linear, PAL. Introduzimos um poset (conjunto parcialmente ordenado) no conjunto das soluções lineares que nos permite comparar também os custos das soluções do problema quadrático, sem o conhecimento prévio das matrizes que definem seus exemplares. Construímos um algoritmo polinomial capaz de determinar pares de permutações livremente comparáveis, conceito apresentado neste trabalho. Provamos um teorema que garante que os custos associados a tais permutações preservam a ordem dada pelo número de inversões das mesmas. Associando soluções do problema a permutações, testes empíricos são apresentados, visando a validação do número de inversões como um parâmetro de referência para a qualidade das soluções. Este trabalho é uma extensão do artigo [RA01] publicado nos anais do XXXIII SBPO, em CD-ROM, 1277-1287, Sobrapo, ILTC, 2001.Palavras-chave: ordenação parcial; problema quadrático de alocação; problema de alocação linear. AbstractWe present an approach to Quadratic Assignment Problem, QAP, via a linear relaxation, through the use of the Linear Assignment Problem, LAP. We define one ordering an LAP-solution-set that makes us compare QAP costs. From here, this poset, partial ordering set, considers coordinates of instances as free variables. We have managed to build a capable algorithm to determine freely comparable permutation pairs. A theorem shows that the order mentioned above is compatible to the one that involves inversion numbers of permutations. We can apply linear and quadratic solutions to permutations and empiric tests are presented to show that the inversion numbers can be used to measure the quality of QAP-solutions. This work is an extension of the article [RA01] published in

show abstract

On the quadratic assignment problem

Cited by 115 publications

References 14 publications

Demand Point Aggregation Analaysis for Location Models

Demand Point Aggregation Analaysis for Location Models

A branch‐and‐bound‐based heuristic for solving the quadratic assignment problem

Ordenações parciais nos conjuntos das soluções dos problemas de alocação linear e quadrático

Contact Info

Product

Resources

About