Stability Analysis of Some Discrete Optimization Algorithms

Authors:
M. V. Devyaterikova;A. A. Kolokolov
Affiliations:
Omsk Affiliated Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Omsk, Russia;Omsk Affiliated Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Omsk, Russia
Venue:
Automation and Remote Control
Year:
2004

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Abstract

Facts established for stability of the relaxation set-based integer programming algorithms were reviewed. For the problem of integer linear programming, the branch-and-bound algorithms were examined for stability within the framework of the Land–Doig method. They were shown to be unstable for sufficiently small oscillations of the relaxation sets of the problems at hand. A similar result was obtained for algorithms with the Dantzig cuts.