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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2017, Volume 27, Issue 4, Pages 540–557 (Mi vuu607)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On one routing problem modeling movement in radiation fields

A. G. Chentsovab, A. A. Chentsova, A. M. Grigoryeva

a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620990, Russia
b Ural Federal University, ul. Mira, 19, Yekaterinburg, 600002, Russia

Abstract: We consider a routing problem with constraints and complicated cost functions. The visited objects are assumed to be clusters, or megalopolises (nonempty finite sets), and the visit to each of them entails certain tasks, which we call interior jobs. The order of visits is subject to precedence constraints. The costs of movements depend on the set of pending tasks (not yet complete at the time of the movement), which is also referred to as “sequence dependence”, “position dependence”, and “state dependence”. Such a dependence arises, in particular, in routing problems concerning emergencies at nuclear power plants, similar to the Chernobyl and Fukushima Daiichi incidents. For example, one could consider a disaster recovery problem concerned with sequential dismantlement of radiation sources; in this case, the crew conducting the dismantlement is exposed to radiation from the sources that have not yet been dealt with. This gives rise to dependence on pending tasks in the cost functions that measure the crew's radiation exposure. The latter dependence reflects the “shutdown” operations for the corresponding radiation sources. This paper sets forth an approach to a parallel solution for this problem, which was implemented and run on the URAN supercomputer.

Keywords: dynamic programming, route, precedence constraints, parallel computation.

Funding Agency Grant Number
Russian Science Foundation 14-11-00109


DOI: https://doi.org/10.20537/vm170405

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Bibliographic databases:

UDC: 519.6
MSC: 49L20, 90C39
Received: 21.08.2017

Citation: A. G. Chentsov, A. A. Chentsov, A. M. Grigoryev, “On one routing problem modeling movement in radiation fields”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:4 (2017), 540–557

Citation in format AMSBIB
\Bibitem{CheCheGri17}
\by A.~G.~Chentsov, A.~A.~Chentsov, A.~M.~Grigoryev
\paper On one routing problem modeling movement in radiation fields
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2017
\vol 27
\issue 4
\pages 540--557
\mathnet{http://mi.mathnet.ru/vuu607}
\crossref{https://doi.org/10.20537/vm170405}
\elib{http://elibrary.ru/item.asp?id=32248456}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Chentsov, A. A. Chentsov, A. M. Grigoriev, “Optimizing the starting point in a precedence constrained routing problem with complicated travel cost functions”, Ural Math. J., 4:2 (2018), 43–55  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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