Tree-search algorithms for quadratic assignment problems

Pierce, J.F.; Crowston, Wallace B. S.

doi:10.1002/nav.3800180102

Cited by 85 publications

(19 citation statements)

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“…The matching in (13.3) of location pairs with facility pairs is sometimes referred to as "pair-assignment;" see, e.g., Pierce and Crowston (1971).…”

Section: Solving the Quadratic Assignment Problem Via Branch-and-boundmentioning

confidence: 99%

“…A similar approach using only a column-reduced matrix was proposed independently by Land (1963); see, e.g., Pierce and Crowston (1971) for further discussion. While Gavett and Plyter's reduction technique gave an easy-to-compute optimal solution to the pair-assignment problem, this solution is often infeasible to the original quadratic assignment problem, resulting in a relatively weak bound; see, e.g., Christofides and Gerrard (1981).…”

Section: Alternative Branch-and-bound Approaches To the Quadratic Assmentioning

confidence: 99%

“…Finally, let P N be the set of permutations on {1, 2, …, N}. With this notation, Gavett and Plyter's relaxed problem is (13.3)The matching in (13.3) of location pairs with facility pairs is sometimes referred to as "pair-assignment;" see, e.g., Pierce and Crowston (1971).As suggested by Conway and Maxwell (1961) and independently established by Gilmore (1962), Gavett and Plyter prove that given two vectors of the same size, if the objective is to sort entries of the vectors so that the dot product is minimized, the solution is found by sorting one vector in nonincreasing order and the other in nondecreasing order. Thus, a permutation minimizes (13.3) when it corresponds to matching sorted elements of {α 1 , α 2 , …, α N } with reversely sorted elements of { 1 ,  2 , …,  N }.…”

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confidence: 99%

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Hub Location Problems: The Location of Interacting Facilities

Kara

Taner

2011

International Series in Operations Research &Amp; Management Science

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), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. PrefaceThis book is the final result of a number of incidents that occurred to us while discussing location issues with colleagues at conferences. Frequently we attended presentations, in which the authors quoted the well-known references that helped to make the discipline what it is today. Upon further inquiry, though, it turned out that some of these colleagues had never actually read the original papers. We then discussed among ourselves which contributions could be credited with shaping the field. And, lo and behold, we found that we, too, had neglected to read some of the papers that form the foundation of our science. Whether it was laziness or other things that got in the way, it had become clear that something had to be done. Our first thought was to collect the original contributions (once we could agree on what they were) and reprint them. When discussing this possibility with a publisher, we immediately ran into a roadblock in the form of copyright. While this appeared to have stopped our enthusiastic effort dead in its tracks, we kept on collecting and reading what we considered original contributions.This went on until we met Camille Price, who suggested that, rather than reprinting the original contributions, we should invite some of the leaders in our field and ask them to describe the original contribution, explain and interpret it, and comment on the impact that it had to the field. This was, of course, an excellent idea, and the response by our colleagues to our pertinent requests was equally enthusiastic. What you hold in your hands is the result of this effort.In other words, the purpose of this book is to provide easy access to the main contributions to location theory. The book is organized as follows. The introductory chapter provides an overview of some of the many facets of location analysis. This is followed by contributions in the main three fields of inquiry: minisum, minimax, and covering problems. The next chapters are part of an ever-growing list of nonstandard location models: models including competitive components, those that locate undesirable facilities, those with probabilistic features, and those that allow interactions between facilities. The following chapters discuss solution techniques: after a discussion of exact and heuristic techniques, we devote an entire chapter to Weiszfeld's method, and another to Lagrangean techniques. The last chapters of this book deal with the spheres of influence that the facilities generate and that attract viii customers to them, an...

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“…The matching in (13.3) of location pairs with facility pairs is sometimes referred to as "pair-assignment;" see, e.g., Pierce and Crowston (1971).…”

Section: Solving the Quadratic Assignment Problem Via Branch-and-boundmentioning

confidence: 99%

Section: Alternative Branch-and-bound Approaches To the Quadratic Assmentioning

confidence: 99%

mentioning

confidence: 99%

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Hub Location Problems: The Location of Interacting Facilities

Kara

Taner

2011

International Series in Operations Research &Amp; Management Science

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“…Unfortunately, no computationally feasible dgo-*Refer to Reference [12] for a survey of computer-aided interconnection routing. tRefer to Reference [14] for an extensive survey of the relevant literature and an excellent bibliography. also letting if component i is assigned to location j…”

Section: Introductionmentioning

confidence: 99%

An n‐step, 2‐variable search algorithm for the component placement problem

Heider

1973

Naval Research Logistics

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The component placement problem is a specialization of the quadratic assignment problem that has been extensively studied for a decade and which is of considerable practical value. Recently, interest in component placement algorithms has risen primarily as a result of increased activity in the field of computer-aided design automation. This paper deals with the methodology of component placement and is based on the results of considerable operational experience. A tutorial presentation of tree search placement algorithms is provided, and an improved placement procedure is described which is demonstrated to be effective in generating near optimal solutions to the component placement problem. These solutions are completely reproducible and are obtained at an acceptable expenditure of computational resources. An additional objective is an assessment of performance of the class of near optimal algorithms. In particular, the question-how close to optimal are the near optimal solutionsis examined.

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“….. 7 Haley (1962Haley ( , 1963 and Pierskalla (1968) Koopmans and Beckmann (1957) also formulated this problem, and later Gilmore (1962), Lawler (1975), Land (1963, Hillier and Connors (1967), Bowman et al (1971), Pierce and Crowston (1971), Gerrard (1976, 1979) and Los (1978) "* carried out further work on quadratic assignment problems (QAP).…”

Section: Chapter II Previous Related Work In Computer Aided Layoutmentioning

confidence: 99%

Computer Aided Layout of Procedure Information for Training and Job Aiding.

Sylla¹,

Babu²

1983

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Tree-search algorithms for quadratic assignment problems

Cited by 85 publications

References 21 publications

Hub Location Problems: The Location of Interacting Facilities

Hub Location Problems: The Location of Interacting Facilities

An n‐step, 2‐variable search algorithm for the component placement problem

Computer Aided Layout of Procedure Information for Training and Job Aiding.

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