Geodesic
On a~measure of quasistability of a~certain vector linearly combinatorial Boolean problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 8-17

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We consider a multicriterion problem of finding the Pareto set in the case when linear forms (functions) are minimized both on a set of substitutions and on a set of Boolean vectors. We obtain a formula for the radius of that type of the problem stability (with respect to perturbations of parameters of a vector criterion) that guarantees the preservation of all Pareto optimal solutions of the initial problem and allows the occurrence of new ones.
Keywords: linearly combinatorial Boolean problem, vector objective function, Pareto set, quasistability radius, perturbing matrix. 
@article{IVM_2010_5_a1,
     author = {V. A. Emelichev and A. V. Karpuk and K. G. Kuz'min},
     title = {On a~measure of quasistability of a~certain vector linearly combinatorial {Boolean} problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {8--17},
     publisher = {mathdoc},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_5_a1/}
}
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V. A. Emelichev; A. V. Karpuk; K. G. Kuz'min. On a~measure of quasistability of a~certain vector linearly combinatorial Boolean problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 8-17. http://geodesic.mathdoc.fr/item/IVM_2010_5_a1/