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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2010 Number 5, Pages 8–17 (Mi ivm6731)

This article is cited in 1 paper

On a measure of quasistability of a certain vector linearly combinatorial Boolean problem

V. A. Emelicheva, A. V. Karpuka, K. G. Kuz'minb

a Chair of Equations of Mathematical Physics, Belarus State University, Minsk, Republic of Belarus
b Chair of General Mathematics and Information Science, Belarus State University, Minsk, Republic of Belarus

Abstract: 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.

UDC: 519.8

Received: 31.03.2008


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:5, 6–14

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