Quasistability of a Vector Trajectory Majority Optimization Problem
Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 38-47.

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We consider a multicriteria combinatorial problem with majority optimality principle whose particular criteria are of the form MINSUM, MINMAX, and MINMIN. We obtain a lower attainable bound for the radius of quasistability of such a problem in the case of the Chebyshev norm on the space of perturbing parameters of the vector criterion. We give sufficient conditions for the quasistability of the problem; these are also necessary in the case of linear special criteria.
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V. A. Emelichev; Yu. v. Stepanishina. Quasistability of a Vector Trajectory Majority Optimization Problem. Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 38-47. http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a3/

[1] Emelichev V. A., Podkopaev D. P., “O kolichestvennoi mere ustoichivosti vektornoi zadachi tselochislennogo programmirovaniya”, ZhVMiMF, 38:11 (1998), 1801–1805 | MR | Zbl

[2] Emelichev V. A., Kravtsov M. K., Podkopaev D. P., “O kvaziustoichivosti traektornykh zadach vektornoi optimizatsii”, Matem. zametki, 63:1 (1998), 21–27 | MR | Zbl

[3] Emelichev V. A., Berdysheva R. A., “O radiusakh ustoichivosti, kvaziustoichivosti i stabilnosti vektornoi traektornoi zadachi leksikograficheskoi optimizatsii”, Diskretnaya matematika, 10:1 (1998), 20–27 | MR | Zbl

[4] Berdysheva R. A., Emelichev V. A., “Nekotorye vidy ustoichivosti kombinatornoi zadachi leksikograficheskoi optimizatsii”, Izv. vuzov. Matem., 1998, no. 12, 11–21 | MR | Zbl

[5] Emelichev V. A., Berdysheva R. A., “Ob ustoichivosti i kvaziustoichivosti traektornoi zadachi posledovatelnoi optimizatsii”, Dokl. NAN Belarusi, 43:3 (1999), 41–44 | MR | Zbl

[6] Emelichev V. A., Berdysheva R. A., “O mere ustoichivosti zadachi tselochislennoi leksikograficheskoi optimizatsii”, Izv. NAN Belarusi. Ser. fiz.-mat. nauk, 1999, no. 4, 119–124 | MR

[7] Leontev V. K., “Ustoichivost v lineinykh diskretnykh zadachakh”, Problemy kibernetiki, 1979, no. 35, 169–184 | MR | Zbl

[8] Emelichev V. A., Stepanishyna Yu. V., “Stability of a majority efficient solution of a vector linear trajectorial problem”, Computer Sci. J. Moldova, 7:3 (1999), 291–307 | MR | Zbl

[9] Mirkin B. G., Problema gruppovogo vybora, Nauka, M., 1974 | Zbl

[10] Sholomov L. A., Logicheskie metody issledovaniya diskretnykh modelei vybora, Nauka, M., 1989 | Zbl

[11] Aizerman M. A., Aleskerov F. T., Vybor variantov: osnovy teorii, Nauka, M., 1990 | Zbl

[12] Mulen E., Kooperativnoe prinyatie reshenii: aksiomy i modeli, Mir, M., 1991

[13] Gordeev E. N., Leontev V. K., “Obschii podkhod k issledovaniyu ustoichivosti reshenii v zadachakh diskretnoi optimizatsii”, ZhVMiMF, 36:1 (1996), 66–72 | MR | Zbl

[14] Artemenko V. I., Gordeev E. N., Zhuravlev Yu. I. i dr., “Metod formirovaniya optimalnykh programmnykh traektorii peremescheniya robota-manipulyatora”, Kibernetika i sistem. analiz, 1996, no. 5, 82–104 | MR

[15] Emelichev V. A., Kravtsov M. K., “O nerazreshimosti vektornykh zadach diskretnoi optimizatsii na sistemakh podmnozhestv v klasse algoritmov lineinoi svertki kriteriev”, Dokl. RAN, 334:1 (1994), 9–11 | MR | Zbl

[16] Emelichev V. A., Kravtsov M. K., “O zadachakh vektornoi diskretnoi optimizatsii na sistemakh podmnozhestv, nerazreshimykh s pomoschyu algoritma lineinoi svertki”, ZhVMiMF, 34:7 (1994), 1082–1094 | MR | Zbl

[17] Emelichev V. A., Kravtsov M. K., “O kombinatornykh zadachakh vektornoi optimizatsii”, Diskretnaya matematika, 7:1 (1995), 3–18 | MR | Zbl

[18] Sotskov Yu. N., Leontev V. K., Gordeev E. N., “Some concepts of stability analysis in combinatorial optimization”, Discrete Appl. Math., 58 (1995), 169–190 | DOI | MR | Zbl

[19] Podinovskii V. V., Nogin V. D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, Nauka, M., 1982 | Zbl

[20] Borda J. C., Memoires sur les elections au scrutin. Histoires de l'academi royale des sciences, Paris, 1781

[21] Condorcet M., Essai sur l'application de l'analyse à la probabilité des decisions rendues à la pluralité des voix, Paris, 1785

[22] Arrow K. J., Social Choice and Individual Values, 2nd edition, John Wiley, New York, 1963

[23] Volskii V. I., Lezina Z. M., Golosovanie v malykh gruppakh: protsedury i metody sravnitelnogo analiza, Nauka, M., 1991

[24] Kozeratskaya L. N., Lebedeva T. T., Sergienko T. I., “Zadachi tselochislennogo programmirovaniya s vektornym kriteriem: parametricheskii analiz i issledovanie ustoichivosti”, Dokl. AN SSSR, 307:3 (1989), 527–529

[25] Sergienko I. V., Kozeratskaya L. N., Lebedeva T. T., Issledovanie ustoichivosti i parametricheskii analiz diskretnykh optimizatsionnykh zadach, Naukova dumka, Kiev, 1995 | Zbl