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 Trudy Inst. Mat. i Mekh. UrO RAN, 2020, Volume 26, Number 3, Pages 219–234 (Mi timm1758)

On the problem of sequential traversal of megalopolises with precedence conditions and cost functions depending on a list of tasks

A. G. Chentsovab, A. A. Chentsova, A. N. Sesekinba

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: A constrained routing problem with complicated cost functions is studied. The construction of the cost functions can be difficult, and therefore the stages of this construction are elements of the solution of the problem. This situation arises, in particular, in studying the engineering problem of dismantling radiation hazardous elements, where, in the framework of a problem statement traditional for discrete optimization, it takes an unacceptably long time to construct a cost matrix whose entries characterize the radiation doses received by performers at the stage of displacement and dismantling. It is assumed that, at the stage of the computational implementation of the resulting optimal algorithm, the corresponding “parts” of the matrix may be not fed to the computer's memory but calculated as needed. Possible applications of the developed methods may be related to the problem of dismantling a decommissioned generator unit of an NPP.

Keywords: dynamic programming, route, Bellman function.

 Funding Agency Grant Number Russian Foundation for Basic Research 19-01-00573 This work was supported by the Russian Foundation for Basic Research (project no. 19-01-00573) and is a part of the research carried out at the Ural Mathematical Center.

DOI: https://doi.org/10.21538/0134-4889-2020-26-3-219-234

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UDC: 517.6
MSC: 05A05, 97N70, 97N80
Revised: 21.07.2020
Accepted:10.08.2020

Citation: A. G. Chentsov, A. A. Chentsov, A. N. Sesekin, “On the problem of sequential traversal of megalopolises with precedence conditions and cost functions depending on a list of tasks”, Trudy Inst. Mat. i Mekh. UrO RAN, 26, no. 3, 2020, 219–234

Citation in format AMSBIB
\Bibitem{CheCheSes20} \by A.~G.~Chentsov, A.~A.~Chentsov, A.~N.~Sesekin \paper On the problem of sequential traversal of megalopolises with precedence conditions and cost functions depending on a list of tasks \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2020 \vol 26 \issue 3 \pages 219--234 \mathnet{http://mi.mathnet.ru/timm1758} \crossref{https://doi.org/10.21538/0134-4889-2020-26-3-219-234} \elib{https://elibrary.ru/item.asp?id=43893876}