Numerical measure of strong stability and strong quasistability in the vector problem of integer linear programming

In this paper we consider a vector integer programming problem with the linear partial criteria. Numerical evaluations of two types of stability of the Pareto set have been found. Usually the stability (quasistability) of a vector optimization problem (see [1-10]) is understood as the property of nonappearance of new optimal solutions (preservation of initial) under small perturbations of the problem’s parameters. When we relax these demands we get the concepts of the strong stability and strong quasistability accordingly (see definitions below), that were introduced first by V.K. Leontev for mono-criterion trajectorial problem in [11]. Later lower and upper bounds (in some cases formulas) for evaluation of radii of the strong stability and strong quasistability in the vector trajectorial problem of lexicographic optimization were obtained in [12]. In this paper we consider a vector integer programming problem with the linear partial criteria. Lower bound of radius of the strong stability and formula for evaluation of radius of the strong quasistability have been found for the case where Chebyshev norm was defined in the space of vector criterion parameters. c ©1999 by V.A.Emelichev, Y.V.Nikulin ∗ This work was partially supported by Fundamental Researches Foundation of Belarus (grant 97-266).