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On necessary and suﬃcient conditions for stability and quasistability in combinatorial multicriteria optimization

Kuzmin K. G., Nikulin Y. V., Makela M. M.

Control and Cybernetics

2017

Vol. 46, no. 4

361--382

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.

The stability radius of an efficient solution in minimax Boolean programming problem

Emelichev V. A., Krichko V. N., Nikulin Y. V.

Control and Cybernetics

2004

Vol. 33, no 1

127-132

We consider a vector minimax Boolean programming problem. The problem consists in finding the set of Pareto optimal solutions. When the problem's parameters vary then the optimal solution of the problem obtained for some initial parameters may appear non-optimal. We calculate the maximal perturbation of parameters which preseves the Optimality of a given solution of the problem. The formula for the stability radius of the given Pareto optimal solution was obtained.