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Home » Issues » Archive of Issues » 2018 - 3 issue » pp. 348-363

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Russia Yekaterinburg
Year
2018
Volume
28
Issue
3
Pages
348-363
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Section Mathematics
Title Dynamic programming in the generalized bottleneck problem and the start point optimization
Author(-s) Chentsov A.G.ab, Chentsov A.A.a, Sesekin A.N.ab
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa, Ural Federal Universityb
Abstract We consider one non-additive routing problem, which is a generalization of the well-known “bottleneck problem”. The parameter is assumed to be a positive number, the degree of which determines the weight of the corresponding stage of the displacement system. By varying the parameter, it is possible to make the initial or, on the contrary, the final stages of displacement dominant. The variant of aggregation of values with the above-mentioned weights corresponds to the ideological formulation of the “bottleneck problem”, but opens the possibility of investigating new versions of routing problems with constraints. It is assumed, however, that the statement of the problem is complicated by the dependence of values on the list of tasks and includes restrictions in the form of precedence conditions. In addition, in the interest of optimization, an arbitrary choice of the initial state from a given a priori set is allowed. For the construction, the apparatus of widely understood dynamic programming is used. The possibility of realizing a global extremum with any degree of accuracy under conditions when the set of possible initial states is not finite is investigated.
Keywords route optimization, dynamic programming, start point optimization
UDC 517.6
MSC 49L20, 90C39
DOI 10.20537/vm180306
Received 6 June 2018
Language Russian
Citation Chentsov A.G., Chentsov A.A., Sesekin A.N. Dynamic programming in the generalized bottleneck problem and the start point optimization, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 3, pp. 348-363.
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