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Cybernetics and Systems Analysis

, Volume 44, Issue 3, pp 397–404 | Cite as

Stability criteria in vector combinatorial bottleneck problems in terms of binary relations

  • V. A. Emelichev
  • K. G. Kuz’min
Article

Abstract

The paper considers a vector (multiobjective) path problem with minimax partial criteria. Solving this problem means finding a Pareto set. Binary relations on a set of paths are used to formulate the necessary and sufficient conditions for five types of problem stability against perturbations of the parameters of a vector criterion. Some sufficient stability conditions in terms of Pareto, Smale, and Slater sets are obtained as corollaries.

Keywords

vector combinatorial problem bottleneck criterion Pareto set problem stability with respect to vector criterion perturbing matrix 

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Belarusian State UniversityMinskBelarus

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