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Exact algorithms for the solution of the grey pattern quadratic assignment problem

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Abstract

We propose an exact algorithm to find the optimal solution to the grey pattern problem which is a special instance of the quadratic assignment problem. A very effective branch and bound algorithm is constructed. The special structure of the problem is exploited and optimal solutions for many problem instances established. One instance based on 64 facilities, organized in an 8 by 8 pattern, that was extensively researched in the literature was optimally solved in 15 s of computer time while existing papers report solution times of hours.

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Authors and Affiliations

  1. Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA, 92834, USA

    Zvi Drezner

  2. Department of Multimedia Engineering, Kaunas University of Technology, Kaunas, Lithuania

    Alfonsas Misevičius & Gintaras Palubeckis

Authors
  1. Zvi Drezner
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  2. Alfonsas Misevičius
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  3. Gintaras Palubeckis
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Corresponding author

Correspondence to Zvi Drezner.

Appendix: Generating the distance matrix

Appendix: Generating the distance matrix

Rather than reading the distance array from a file, the array can be easily generated by the following code. It is assumed that \(n_1=n_2\). nsq is the square root of n (equal to \(n_1\)) and is prompted as input. The variables n, i, j, ir, ic, jr, jc are integers and nsq, dr, dc are real. The array d can be integer or real. Double precision is used for real numbers. The code is given in Fig. 11.

Fig. 11
figure 11

Generating the distance matrix

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Drezner, Z., Misevičius, A. & Palubeckis, G. Exact algorithms for the solution of the grey pattern quadratic assignment problem. Math Meth Oper Res 82, 85–105 (2015). https://doi.org/10.1007/s00186-015-0505-1

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  • DOI: https://doi.org/10.1007/s00186-015-0505-1

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