The continuous grey pattern problem |
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Authors: | Zvi Drezner Pawel Kalczynski |
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Institution: | 1.Steven G. Mihaylo College of Business and Economics,California State University-Fullerton,Fullerton,USA |
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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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