Abstract
Problems of optimal object location in a plane outside rectangular forbidden gaps are considered. Objects under location are connected with one another and with the objects, located in the same plane. The criteria are the minimization of maximal weighted distance or total cost of the links between objects. A model building procedure of integer linear programming of the problems above for rectangular metric is given. Solution algorithms are briefly described. The outcomes of a numerical experiment are given.
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Zabudskii, G.G., A Minimax Planar Location Problem with Forbidden Zones: Its Solution Algorithm, Avtom. Telemekh., 2004, no. 2, pp. 93–100.
Morris, J.G., A Linear Programming Approach to the Solution of Constrained Multi-Facility Minimax Location Problems, Where Distances are Rectangular, Oper. Res. Quar., 1973, vol. 24, pp. 419–435.
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Preparata, F.P. and Shamos, M.G., Computational Geometry. An Introduction, New York: Springer, 1985. Translated under the title Vychislitel’naya geometriya: vvedenie, Moscow: Mir, 1989.
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Original Russian Text © G.G. Zabudskii, 2006, published in Avtomatika i Telemekhanika, 2006, No. 12, pp. 136–141.
The work was supported by the Russian Humanitarian Scientific Foundation, project no. 04-02-00238a.
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Zabudskii, G.G. Model building and location problem solving in a plane with forbidden gaps. Autom Remote Control 67, 1986–1990 (2006). https://doi.org/10.1134/S0005117906120101
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DOI: https://doi.org/10.1134/S0005117906120101