We consider a multiple objective combinatorial optimization problem with an arbitrary vector-criterion. The necessary and sufficient conditions for stability and quasistability are obtained for large classes of problems with partial criteria possessing certain properties of regularity.
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.
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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.
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