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1
Content available Post-optimal analysis for multicriteria integer linear programming problem of finding extreme solutions
Emelichev V. A., Nikulin Y.
Control and Cybernetics
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2018
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Vol. 47, no. 3
225--238
EN
We consider a multicriteria problem of integer linear programming and study the set of all individual criterion minimizers (extreme solutions) playing an important role in determining the range of Pareto optimal set. In this work, the lower and upper attainable bounds on the stability radius of the set of extreme solutions are obtained in the situation where solution and criterion spaces are endowed with various H¨older’s norms. In addition, the case of the Boolean problem is analyzed. Some computational challenges are also discussed.
2
Content available Qualitative stability analysis of multicriteria combinatorial minimin problems
Emelichev V. A., Karelkina O. V., Kuzmin K. G.
Control and Cybernetics
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2012
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Vol. 41, no. 1
57-79
EN
A multicriteria combinatorial problem with minimin partial criteria is considered. Necessary and sufficient conditions for the five known stability types of the problem are obtained. These stability types describe in different ways the behavior of the Pareto and lexicographic sets of the problem under initial data perturba- tions of the vector criteria.
3
Content available remote On stability of some lexicographic integer optimization problem
Emelichev V. A., Gurevsky E. E., Kuzmin K. G.
Control and Cybernetics
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2010
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Vol. 39, no 3
811-826
EN
A lexicographic integer optimization problem with criteria represented by absolute values of linear functions is considered. Five types of stability for the set of lexicographic optima under small changes of the parameters of the vector criterion are investigated.
4
Content available remote On stability of some lexicographic multicriteria Boolean problem
Emelichev V. A., Gurevsky E. E.
Control and Cybernetics
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2007
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Vol. 36, no 2
333-346
EN
We consider a multicriteria lexicographic Boolean problem of minimizing absolute deviations of linear functions from zero. We investigate the stability radius which can be understood as a limit level of independent perturbations of the parameters, for which new lexicographic optima do not appear. Lower and upper accessible bounds of the stability radius are obtained.
5
Content available remote The stability radius of an efficient solution in minimax Boolean programming problem
Emelichev V. A., Krichko V. N., Nikulin Y. V.
Control and Cybernetics
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2004
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Vol. 33, no 1
127-132
EN
We consider a vector minimax Boolean programming problem. The problem consists in finding the set of Pareto optimal solutions. When the problem's parameters vary then the optimal solution of the problem obtained for some initial parameters may appear non-optimal. We calculate the maximal perturbation of parameters which preseves the Optimality of a given solution of the problem. The formula for the stability radius of the given Pareto optimal solution was obtained.
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