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Model. Anal. Inform. Sist., 2016, Volume 23, Number 2, Pages 211–227 (Mi mais492)  

Routization problem complicated by the dependence of costs functions and «current» restrictions from the tasks list

A. G. Chentsovab, A. A. Chentsova

a N.N. Krasovskii Institute of Mathematics and Mechanics, S. Kovalevskaya str., 16, Ekaterinburg, 620990, Russia
b Ural Federal University, Mira str., 19, Ekaterinburg, 620002, Russia

Abstract: The problem of a routization of the movements complicated by the restrictions of different type (preceding conditions, the restrictions on the attainability of states by each movement and others) is considered. A multivariance at the movement step is permitted, it is naturally resulted in the problem about the visiting of megalopolises. The costs of movements and jobs executed when visiting megalopolises may depend on the list of tacks. This list may correspond to performed or unperformed tasks. "Current" restrictions (on movements) may depend on the aforementioned list of tasks. The considered setting is oriented to the application with regard to a nuclear power engineering problems (the problem of decreasing irradiation of the nuclear power station staff when executing a complex of tasks under high radiation intensity) and the machine building. In the second case, which consists in controling a machine for the sheet cutting of details by the numerical program control machines, "current" restrictions on movements may be conditioned by temperature tolerance relative to the fragments of sheet which have already been "visited" by the cutting machine. The scheme of constructing the optimal solution based on the widely understood dynamic programming is considered in this article. The used algorithm is realized on a personal computer; the results of its application are illustrated by the modelling examples.

Keywords: route, trace, preceding conditions.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-08-00419_а
15-01-07909_а
Ministry of Education and Science of the Russian Federation 02.A03.21.0006
This work was supported by the Federal targeted Program "Mathematical problems of modern control theory". This work was supported by the Russian foundation for basic reseach (projects 14-08-00419, 15-01-07909). This work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006


DOI: https://doi.org/10.18255/1818-1015-2016-2-211-227

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Bibliographic databases:

UDC: 519.6
Received: 28.11.2015

Citation: A. G. Chentsov, A. A. Chentsov, “Routization problem complicated by the dependence of costs functions and «current» restrictions from the tasks list”, Model. Anal. Inform. Sist., 23:2 (2016), 211–227

Citation in format AMSBIB
\Bibitem{CheChe16}
\by A.~G.~Chentsov, A.~A.~Chentsov
\paper Routization problem complicated by the dependence of costs functions and <<current>> restrictions from the tasks list
\jour Model. Anal. Inform. Sist.
\yr 2016
\vol 23
\issue 2
\pages 211--227
\mathnet{http://mi.mathnet.ru/mais492}
\crossref{https://doi.org/10.18255/1818-1015-2016-2-211-227}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3504590}
\elib{http://elibrary.ru/item.asp?id=25810353}


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