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 Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 1, Pages 41–54 (Mi ivm8861)

Finding and analysis of estimation of the number of iterations in integer programming algorithms using the regular partitioning method

A. A. Kolokolovab, L. A. Zaozerskayaab

a Chair of Applied and Computational Mathematics, Omsk State University
b Discrete Optimization Laboratory, Omsk Branch of Sobolev Institute of Mathematics SB RAS, 13 Pevtsov str., Omsk, 644043 Russia

Abstract: We review the results of studying integer linear programming algorithms which exploit properties of problem relaxation sets. The main attention is paid to the estimation of the number of iterations of these algorithms by means of the regular partitions method and other approaches. We present such estimates for some cutting plane, branch and bound (Land and Doig scheme), and $L$-class enumeration algorithms and consider questions of their stability. We establish the upper bounds for the average number of iterations of the mentioned algorithms as applied to the knapsack problem and the set packing one.

Keywords: discrete optimization, integer programming, regular partitions method, estimates of the number of iterations, cuts, $L$-class enumeration, branch and bound method, estimates on average, stability of algorithms.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:1, 35–46

UDC: 519.8

Citation: A. A. Kolokolov, L. A. Zaozerskaya, “Finding and analysis of estimation of the number of iterations in integer programming algorithms using the regular partitioning method”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 1, 41–54; Russian Math. (Iz. VUZ), 58:1 (2014), 35–46

Citation in format AMSBIB
\Bibitem{KolZao14} \by A.~A.~Kolokolov, L.~A.~Zaozerskaya \paper Finding and analysis of estimation of the number of iterations in integer programming algorithms using the regular partitioning method \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2014 \issue 1 \pages 41--54 \mathnet{http://mi.mathnet.ru/ivm8861} \transl \jour Russian Math. (Iz. VUZ) \yr 2014 \vol 58 \issue 1 \pages 35--46 \crossref{https://doi.org/10.3103/S1066369X14010046} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84892530380} 

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This publication is cited in the following articles:
1. A. A. Kolokolov, L. A. Zaozerskaya, “Analysis of some cutting plane algorithms of integer programming”, 2016 Dynamics of Systems, Mechanisms and Machines, DYNAMICS 2016, ed. A. Kosykh, IEEE
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