Stability criteria in vector combinatorial bottleneck problems in terms of binary relations
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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.
Keywordsvector combinatorial problem bottleneck criterion Pareto set problem stability with respect to vector criterion perturbing matrix
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- 4.I. V. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability and Parametric Analyses of Discrete Optimization Problems [in Russian], Naukova Dumka, Kyiv (1995).Google Scholar
- 5.I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems. Challenges, Solution Techniques, and Investigations [in Russian], Naukova Dumka, Kyiv (2003).Google Scholar
- 7.B. A. Berezovskii, V. I. Borzenko, and L. N. Kempner, Binary Relations in Multiobjective Optimization [in Russian], Nauka, Moscow (1981).Google Scholar
- 8.V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multiobjective Problems [in Russian], Nauka, Moscow (1982).Google Scholar
- 9.L. A. Sholomov, “Studying relations in criterion spaces and synthesis of multiple-choice operators,” in: Mathematical Problems in Cybernetics [in Russian], Issue 5, 109–143 (1994).Google Scholar