Estimation of the number of iterations in integer programming algorithms using the regular partitions method

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 es...

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Vydáno v:Russian mathematics Ročník 58; číslo 1; s. 35 - 46
Hlavní autoři: Kolokolov, A. A., Zaozerskaya, L. A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.01.2014
Témata:
Mathematics
Mathematics and Statistics
integer programming
estimates of the number of iterations
regular partitions method
discrete optimization
branch and bound method
L-class enumeration
stability of algorithms
estimates on average
cuts
ISSN:1066-369X, 1934-810X
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Popis
Shrnutí: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.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X14010046