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Qualitative stability analysis of multicriteria combinatorial minimin problems

Emelichev V. A., Karelkina O. V., Kuzmin K. G.

Control and Cybernetics

2012

Vol. 41, no. 1

57-79

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.

On stability of some lexicographic multicriteria Boolean problem

Emelichev V. A., Gurevsky E. E.

Control and Cybernetics

2007

Vol. 36, no 2

333-346

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.