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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 3, Pages 348–363 (Mi vuu643)  

MATHEMATICS

Dynamic programming in the generalized bottleneck problem and the start point optimization

A. G. Chentsovab, A. A. Chentsovb, A. N. Sesekinba

a Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia
b N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia

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.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 30
The work was supported by the Presidium of the Russian Academy of Sciences, project no. 30 “Theory and Technology of Multilevel Decentralized Group Control in Conditions of Conflict and Cooperation”.


DOI: https://doi.org/10.20537/vm180306

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Document Type: Article
UDC: 517.6
MSC: 49L20, 90C39
Received: 06.06.2018

Citation: A. G. Chentsov, A. A. Chentsov, A. N. Sesekin, “Dynamic programming in the generalized bottleneck problem and the start point optimization”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:3 (2018), 348–363

Citation in format AMSBIB
\Bibitem{CheCheSes18}
\by A.~G.~Chentsov, A.~A.~Chentsov, A.~N.~Sesekin
\paper Dynamic programming in the generalized bottleneck problem and the start point optimization
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 3
\pages 348--363
\mathnet{http://mi.mathnet.ru/vuu643}
\crossref{https://doi.org/10.20537/vm180306}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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