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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 4, Pages 23–32 (Mi ivm7288)  
This article is cited in 3 scientific papers (total in 3 papers)

The analysis of the stability of some integer programming algorithms with respect to the objective function

M. V. Devyaterikovaa, A. A. Kolokolovbc, N. A. Kosarevc

a Chair of Applied Mathematics and Information Systems, Omsk State Technical University, Omsk, Russia
b Chair of Applied and Calculus Mathematics, Omsk State University, Omsk, Russia
c Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Omsk, Russia
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Abstract: In this paper we define the notion of the stability with respect to the objective function for a wide class of integer linear programming algorithms. We study the stability of some of them under small variations of coefficients in the objective function. We prove the existence of both stable and unstable versions of the $L$-class enumeration algorithms. We show that some branch and bound algorithms, as well as some decomposition algorithms with Benders cuts, are unstable. We propose a modification of the considered decomposition algorithms that makes the latter stable with respect to the objective function.
Keywords: discrete optimization, integer programming, stability of algorithms, $L$-class enumeration, branch and bound method, Benders decomposition.
Received: 20.10.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 4, Pages 18–25
DOI: https://doi.org/10.3103/S1066369X11040049
Bibliographic databases:
Document Type: Article
UDC: 519.854
Language: Russian
Citation: M. V. Devyaterikova, A. A. Kolokolov, N. A. Kosarev, “The analysis of the stability of some integer programming algorithms with respect to the objective function”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 4, 23–32; Russian Math. (Iz. VUZ), 55:4 (2011), 18–25
Citation in format AMSBIB
\Bibitem{DevKolKos11}
\by M.~V.~Devyaterikova, A.~A.~Kolokolov, N.~A.~Kosarev
\paper The analysis of the stability of some integer programming algorithms with respect to the objective function
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 4
\pages 23--32
\mathnet{http://mi.mathnet.ru/ivm7288}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2919794}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 4
\pages 18--25
\crossref{https://doi.org/10.3103/S1066369X11040049}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958725019}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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