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The continuous grey pattern problem

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Journal of the Operational Research Society

Abstract

A new location problem is formulated and solved. It is the continuous version of the grey pattern problem which is a special case of the Quadratic Assignment Problem. The problem is a minimization of a convex function subject to non-convex constraints and has infinitely many optimal solutions. We propose several mathematical programming formulations that are suitable for a multi-start heuristic algorithm. In addition to solving these formulations by the Solver in Excel and Mathematica, a special Nelder–Mead algorithm is proposed. This special algorithm provided the best results. One suggested modification may improve the performance of the Nelder–Mead algorithm for other optimization problems as well.

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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 & Pawel Kalczynski

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  1. Zvi Drezner
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  2. Pawel Kalczynski
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Correspondence to Zvi Drezner.

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Drezner, Z., Kalczynski, P. The continuous grey pattern problem. J Oper Res Soc 68, 469–483 (2017). https://doi.org/10.1057/s41274-016-0023-4

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  • DOI: https://doi.org/10.1057/s41274-016-0023-4

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