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An Algorithm for the Quadratic Assignment Problem

Author

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  • G. W. Graves

    (Graduate School of Business, University of California, Los Angeles)

  • A. B. Whinston

    (Krannert Graduate School, Purdue)

Abstract

The paper presents a new approach to solving a class of combinatorial economic allocation problems. One member of this class is known as the quadratic assignment problem. Besides presenting an algorithm to solve this problem, we will discuss in general terms the techniques for treating combinatorial problems. A novel feature of the paper is the development of the statistical properties of the criterion function. These statistical properties are used in conjunction with a general enumerative procedure to form the main parts of the algorithm. Using the idea of confidence level enumeration, an extension of the algorithm is proposed which should allow for the effective treatment of large scale combinatorial problems. Finally we present some computational results in order to illustrate the effectiveness of the general approach.

Suggested Citation

  • G. W. Graves & A. B. Whinston, 1970. "An Algorithm for the Quadratic Assignment Problem," Management Science, INFORMS, vol. 16(7), pages 453-471, March.
    • Handle: RePEc:inm:ormnsc:v:16:y:1970:i:7:p:453-471
    DOI: 10.1287/mnsc.16.7.453
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    Cited by:

    1. Balakrishnan, Jaydeep & Cheng, Chun Hung, 1998. "Dynamic layout algorithms: a state-of-the-art survey," Omega, Elsevier, vol. 26(4), pages 507-521, August.
    2. Loiola, Eliane Maria & de Abreu, Nair Maria Maia & Boaventura-Netto, Paulo Oswaldo & Hahn, Peter & Querido, Tania, 2007. "A survey for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 176(2), pages 657-690, January.
    3. Frank B. Baker & Lawrence J. Hubert, 1981. "The Analysis of Social Interaction Data," Sociological Methods & Research, , vol. 9(3), pages 339-361, February.
    4. Alexander Barvinok & Tamon Stephen, 2003. "The Distribution of Values in the Quadratic Assignment Problem," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 64-91, February.
    5. Tian, Xiaopeng & Niu, Huimin, 2020. "Optimization of demand-oriented train timetables under overtaking operations: A surrogate-dual-variable column generation for eliminating indivisibility," Transportation Research Part B: Methodological, Elsevier, vol. 142(C), pages 143-173.
    6. Lawrence Hubert, 1979. "Matching models in the analysis of cross-classifications," Psychometrika, Springer;The Psychometric Society, vol. 44(1), pages 21-41, March.

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