Abstract:
We consider a multicriteria formulation of the well-known
combinatorial problem to minimise a linear form over an arbitrary
set of permutations of the symmetric group.
We give bounds (in the Chebyshev metric) for the coefficients
of the linear forms preserving the corresponding efficiency
of an arbitrary solution that is Pareto-, Slater-, or Smale-optimal.
We present some conditions
guaranteeing that a permutation possessing the efficiency property
is locally stable. The class of quasi-stable problems is described.
Received: 24.06.2000
Bibliographic databases:
UDC:
519.10
Language: Russian
Citation:
V. A. Emelichev, V. G. Pokhil'ko, “Analysis of the sensitivity of efficient solutions of a vector problem of minimizing linear forms on a set of permutations”, Diskr. Mat., 12:3 (2000), 37–48; Discrete Math. Appl., 10:4 (2000), 367–378
\Bibitem{EmePok00}
\by V.~A.~Emelichev, V.~G.~Pokhil'ko
\paper Analysis of the sensitivity of efficient solutions of a vector problem of minimizing linear forms on a set of permutations
\jour Diskr. Mat.
\yr 2000
\vol 12
\issue 3
\pages 37--48
\mathnet{http://mi.mathnet.ru/dm339}
\crossref{https://doi.org/10.4213/dm339}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1810952}
\zmath{https://zbmath.org/?q=an:0981.90051}
\transl
\jour Discrete Math. Appl.
\yr 2000
\vol 10
\issue 4
\pages 367--378
Linking options:
https://www.mathnet.ru/eng/dm339
https://doi.org/10.4213/dm339
https://www.mathnet.ru/eng/dm/v12/i3/p37
This publication is cited in the following 9 articles:
V. A. Emelichev, V. V. Korotkov, “On the stability radius of an efficient solution of a multicriteria portfolio optimisation problem with the Savage criteria”, Discrete Math. Appl., 21:5-6 (2011), 509–515
Emelichev V., Kuz'Min K., Nikulin Y., “Stability analysis of the Pareto optimal solutions for some vector boolean optimization problem”, Optimization, 54:6 (2005), 545–561
V. A. Emelichev, K. G. Kuzmin, “Stability Radius of a Lexicographic Optimum of a Vector Problem of Boolean Programming”, Cybern Syst Anal, 41:2 (2005), 215
V. A. Emelichev, K. G. Kuz'min, “Stability analysis of a strictly efficient solution of a vector problem of Boolean programming in the metric $l_1$”, Discrete Math. Appl., 14:5 (2004), 521–526
V. A. Emelichev, K. G. Kuz'min, A. M. Leonovich, “On a type of stability for a vector combinatorial problem with partial criteria of the form $\Sigma$-MINMAX and $\Sigma$-MINMIN”, Russian Math. (Iz. VUZ), 48:12 (2004), 15–25
V. A. Emelichev, K. G. Kuz'min, A. M. Leonovich, “Stability in the combinatorial vector optimization problems”, Autom. Remote Control, 65:2 (2004), 227–240
S. E. Bukhtoyarov, V. A. Emelichev, “Parametrizatsiya printsipa optimalnosti (“ot Pareto do Sleitera”) i ustoichivost
mnogokriterialnykh traektornykh zadach”, Diskretn. analiz i issled. oper., ser. 2, ser. 2, 10:2 (2003), 3–18
Emelichev V.A., Girlich E., Nikulin Y.V., Podkopaev D.P., “Stability and regularization of vector problems of integer linear programming”, Optimization, 51:4 (2002), 645–676
V. A. Emelichev, Yu. v. Stepanishina, “Multicriteria combinatorial linear problems: parametrisation of the optimality principle and the stability of the effective solutions”, Discrete Math. Appl., 11:5 (2001), 435–444
Citation in format AMSBIB
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