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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2016, Volume 26, Issue 4, Pages 565–578 (Mi vuu561)  

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

The Bellmann insertions in route problems with constraints and complicated cost functions. II

A. G. Chentsovab

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, 620002, Russia

Abstract: The route problem with precedence conditions and cost functions depending on the jobs list is considered; these singularities correspond to engineering applications. In particular, the above-mentioned singularities exist in statements of some problems arising in nuclear energetics and in machines with numerical control. Problems involved in sequentially circuiting megalopolises and in carrying out some (interior) work during these circuits are investigated. A procedure for local improvement of heuristic solutions for problems of perceptible dimension is proposed; this procedure exploits insertions on the dynamic programming base. Dynamic programming is realized in the form of a variant that does not provide for construction of a “full” array of values of the Bellman function. The search for localization of an insertion involves restricting to the variant of the Bellman procedure that realizes the extremum of the (local) criterion without constructing a corresponding solution in the form of a route-track pair. A more complete and more cost-intensive (in the sense of memory resources) procedure including determination of the above-mentioned (local optimal) solution is planned after the choice of the insertion localization.

Keywords: insertion, dynamic programming, route.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-07909_а
16-01-00505_а
16-01-00649_а


DOI: https://doi.org/10.20537/vm160410

Full text: PDF file (315 kB)
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Bibliographic databases:

UDC: 519.6
MSC: 28A33
Received: 15.10.2016

Citation: A. G. Chentsov, “The Bellmann insertions in route problems with constraints and complicated cost functions. II”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:4 (2016), 565–578

Citation in format AMSBIB
\Bibitem{Che16}
\by A.~G.~Chentsov
\paper The Bellmann insertions in route problems with constraints and complicated cost functions.~II
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2016
\vol 26
\issue 4
\pages 565--578
\mathnet{http://mi.mathnet.ru/vuu561}
\crossref{https://doi.org/10.20537/vm160410}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3604256}
\elib{http://elibrary.ru/item.asp?id=27673741}


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    This publication is cited in the following articles:
    1. A. G. Chentsov, A. A. Chentsov, “Modelnyi variant zadachi o posledovatelnoi utilizatsii istochnikov izlucheniya (iteratsii na osnove optimiziruyuschikh vstavok)”, Izv. IMI UdGU, 50 (2017), 83–109  mathnet  crossref  elib
    2. A. G. Chentsov, A. M. Grigorev, “Optimiziruyuschie multivstavki v zadachakh marshrutizatsii s ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:4 (2018), 513–530  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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