**Authors:** Vladimir A.Emelichev, Sergey E.Bukhtoyarov

### Abstract

We consider a multicriteria integer linear programming problem with a parametrized optimality
principle which is implemented by means of partitioning the partial criteria set into non-empty subsets,
inside which relations on the set of solutions are based on the Pareto minimum. The introduction of this
principle allows us to connect such classical selection functions as Pareto and aggregative-extremal.
A quantitative analysis of two types of stability of the problem to perturbations of the parameters of
objective functions is given under the assumption that an arbitrary $l_p$-H\"{o}lder norm,
$1\leq p\leq\infty,$ is given in the solution space, and the Chebyshev norm is given in the criteria space.
The formulas for the radii of quasistability and strong quasi-stability are obtained. Criteria of these
types of stability are given as corollaries.

Belarusian State University,

av. Nezavisimosti,4, 220030 Minsk

Belarus

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