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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 4, Pages 270–289 (Mi timm443)  

This article is cited in 8 scientific papers (total in 8 papers)

Iteration method in the routing problem with internal losses

A. A. Chentsov, A. G. Chentsov, P. A. Chentsov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: The problem of a sequential traversal of sets is considered, which is complicated by the necessity of fulfilling (internal) tasks on the sets as well as by restrictions in the form of precedence conditions. It is assumed that the method of aggregating the losses is additive. For the appearing extremal problem with dependent variables, an equivalent transformation is built for the optimization problem on a Cartesian product. Based on this, an iteration method is constructed that uses a reconstructible model of the courier problem (a traveling salesman problem complicated by precedence conditions).

Keywords: route, path, precedence conditions.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 269, suppl. 1, S48–S68

UDC: 519.6
Received: 10.03.2009

Citation: A. A. Chentsov, A. G. Chentsov, P. A. Chentsov, “Iteration method in the routing problem with internal losses”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 270–289; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S48–S68

Citation in format AMSBIB
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\by A.~A.~Chentsov, A.~G.~Chentsov, P.~A.~Chentsov
\paper Iteration method in the routing problem with internal losses
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 4
\pages 270--289
\mathnet{http://mi.mathnet.ru/timm443}
\elib{http://elibrary.ru/item.asp?id=12952772}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S48--S68
\crossref{https://doi.org/10.1134/S0081543810060064}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962467093}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Chentsov, A. G. Chentsov, “On an iterative procedure for solving a routing problem with constraints”, Proc. Steklov Inst. Math. (Suppl.), 283, suppl. 1 (2013), 24–45  mathnet  crossref  isi  elib
    2. A. G. Chentsov, P. A. Chentsov, “Ob odnoi nestatsionarnoi zadache marshrutizatsii s ogranicheniyami”, Model. i analiz inform. sistem, 19:4 (2012), 5–24  mathnet
    3. Salii Ya.V., Chentsov A.G., “Ob odnoi marshrutnoi zadache na uzkie mesta s vnutrennimi rabotami”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 17:3 (2012), 827–847  elib
    4. A. A. Chentsov, A. G. Chentsov, P. A. Chentsov, “Elements of dynamic programming in extremal route problems”, Autom. Remote Control, 75:3 (2014), 537–550  mathnet  crossref  isi
    5. A. A. Chentsov, A. G. Chentsov, “Metod iteratsii v obobschennoi zadache kurera s osobennostyu v opredelenii funktsii stoimosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 3, 88–113  mathnet
    6. Chentsov A.G., Chentsov A.A., “Dynamic Programming in the Routing Problem with Constraints and Costs Depending on a List of Tasks”, Dokl. Math., 88:3 (2013), 637–640  crossref  mathscinet  zmath  isi  elib  scopus
    7. A. A. Petunin, A. G. Chentsov, P. A. Chentsov, “Lokalnye vstavki na osnove dinamicheskogo programmirovaniya v zadache marshrutizatsii s ogranicheniyami”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 56–75  mathnet
    8. A. A. Petunin, A. A. Chentsov, A. G. Chentsov, P. A. Chentsov, “Elements of dynamic programming in local improvement constructions for heuristic solutions of routing problems with constraints”, Autom. Remote Control, 78:4 (2017), 666–681  mathnet  crossref  isi  elib
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