Several kinds of Stability of efficient Solutions in Vector Trajectorial discrete Optimization Problem

Emelichev, V. A.; Girlich, E.; Podkopaev, D. P.

This work was partially supported by DAAD, Fundamental Researches Foundation of Belarus and International Soros Science Education Program We consider a vector discrete optimization problem on a system of non- empty subsets (trajectories) of a finite set. The vector criterion of the pro- blem consists partial criterias of the kinds MINSUM, MINMAX and MIN- MIN. The stability of eficient (Pareto optimal, Slater optimal and Smale op- timal) trajectories to perturbations of vector criterion parameters has been investigated. Suficient and necessary conditions of eficient trajectories local stability have been obtained. Lower evaluations of eficient trajectories sta- bility radii, and formulas in several cases, have been found for the case when l(inf) -norm is defined in the space of vector criterion parameters.

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Emelichev, V. A. / Girlich, E. / Podkopaev, D. P.: Several kinds of Stability of efficient Solutions in Vector Trajectorial discrete Optimization Problem. 2005.

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