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Russia Yekaterinburg
Section Mathematics
Title Routing of displacements with dynamic constraints: “bottleneck problem”
Author(-s) Chentsov A.G.ab, Chentsov A.A.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract A complicated variant of the “bottleneck problem” is considered, namely: the problem of sequential visiting of megalopolises with preceding constraints. It is supposed that costs functions and “current” constraints with respect to displacements selection depend on the tasks list which is not completed at the moment. The variant of widely understood dynamic programming is proposed, it doesn't foresee (with preceding conditions) construction of the whole array of the Bellman function values; the special layers of this function realizing in its totality the partial array of its values are constructed (it helps to decrease the calculation complexity). An algorithm of the problem value (global extremum) calculation is proposed, the computer realization of which implies the existence of only one layer of the Bellman function in a memory of computer; the obtained value may be used for the heuristics testing. The optimal algorithm of “complete” solving of the route problem is constructed, within which all layers of the Bellman function are used at the route and trace constructing.
Keywords route, trace, preceding conditions, dynamic programming
UDC 519.6
MSC 05A05, 97N70, 97N80
DOI 10.20537/vm160110
Received 27 February 2016
Language Russian
Citation Chentsov A.G., Chentsov A.A. Routing of displacements with dynamic constraints: “bottleneck problem”, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 1, pp. 121-140.
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  3. Chentsov A.A., Chentsov A.G. Route problem in which cost functions and “current” constraints depend from tasks list, Vestn. Tambov. Univ. Ser. Estestv. Tekh. Nauki, 2015, vol. 20, no. 5, pp. 1521-1525 (in Russian).
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  6. Petunin A.A., Chentsov A.G., Chentsov P.A. To the question about instrument routing in the automated machines of the sheet cutting, St. Petersburg State Polytechnical University Journal. Computer Science. Telecommunication and Control Systems, 2013, issue 2 (169), pp. 103-111 (in Russian).
  7. Chentsov A.G., Salii Ya.V. A model of “nonadditive” routing problem where the costs depend on the set of pending tasks, Vestn. Yuzhno-Ural. Gos. Univ., Ser. Mat. Model. Program., 2015, vol. 8, no. 1, pp. 24-45.
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