Об одном типе устойчивости векторной комбинаторной задачи размещения

A. G. Vodennikov ; V. A. Emelichev ; K. G. Kuz'min

Diskretnyj analiz i issledovanie operacij, Tome 14 (2007) no. 2, pp. 32-40.

Bibliographie

[1] Girlikh E., Kovalev M. N., Kravtsov M. K., “Stabilnost, ustoichivost i kvaziustoichivost mnogokriterialnoi zadachi na sisteme podmnozhestv”, Kibernetika i sistemnyi analiz, 1999, no. 5, 111–124 | MR

[2] Gordeev E. N., Leontev V. K., “Obschii podkhod k issledovaniyu ustoichivosti reshenii v zadachakh diskretnoi optimizatsii”, Zhurn. vychisl. matematiki i matem. fiziki, 36:1 (1996), 66–72 | MR | Zbl

[3] Gurevskii E. E., Emelichev V. A., “Ob ustoichivosti vektornoi bulevoi zadachi minimizatsii absolyutnykh uklonenii ot nulya lineinykh funktsii”, Izvestiya vuzov. Matematika, 2006, no. 12, 27–32 | MR

[4] Emelichev V. A., Gurevskii E. E., “Ob ustoichivosti vektornoi kombinatornoi zadachi razbieniya”, Kibernetika i sistemnyi analiz, 2007, no. 3, 177–181 | MR | Zbl

[5] Emelichev V. A., Kuzmin K. G., “Analiz chuvstvitelnosti effektivnogo resheniya vektornoi bulevoi zadachi minimizatsii proektsii lineinykh funktsii na $\mathbb R_+$ i $\mathbb R_-$”, Diskret. analiz i issled. operatsii. Ser. 2, 12:2 (2005), 24–43 | MR

[6] Emelichev V. A., Kuzmin K. G., “O kvaziustoichivosti vektornoi bulevoi zadachi minimizatsii porogovykh funktsii”, Vestsi NAN Belarusi. Ser. fiz.-mat. navuk, 2005, no. 4, 55–58 | MR

[7] Emelichev V. A., Kuzmin K. G., “O radiuse ustoichivosti leksikograficheskogo optimuma odnoi vektornoi zadachi buleva programmirovaniya”, Kibernetika i sistemnyi analiz, 2005, no. 2, 71–80 | MR

[8] Emelichev V. A., Kuzmin K. G., Leonovich A. M., “Ob odnom tipe ustoichivosti vektornoi kombinatornoi zadachi s chastnymi kriteriyami vida $\Sigma$-MINMAX i $\Sigma$-MINMIN”, Izvestiya vuzov. Matematika, 2004, no. 12, 17–27 | MR

[9] Emelichev V. A., Kuzmin K. G., Leonovich A. M., “Ustoichivost v vektornykh kombinatornykh zadachakh optimizatsii”, Avtomatika i telemekhanika, 2004, no. 2, 79–92 | MR | Zbl

[10] Emelichev V. A., Podkopaev D. P., “Ustoichivost i regulyarizatsiya vektornykh zadach tselochislennogo lineinogo programmirovaniya”, Diskret. analiz i issled. operatsii. Ser. 2, 8:1 (2001), 47–69 | MR | Zbl

[11] Emelichev V. A., Stepanishina Yu. V., “Kvaziustoichivost vektornoi nelineinoi traektornoi zadachi s paretovskim printsipom optimalnosti”, Izv. vuzov. Matematika, 2000, no. 12, 27–32 | MR | Zbl

[12] Emelichev V. A., Stepanishina Yu. V., “Kriterii kvaziustoichivosti vektornoi traektornoi zadachi s mazhoritarnym printsipom optimalnosti”, Kibernetika i sistemnyi analiz, 2001, no. 5, 63–71 | MR | Zbl

[13] Kristofides N., Teoriya grafov. Algoritmicheskii podkhod, Mir, M., 1978 | MR

[14] Lebedeva T. T., Sergienko T. I., “Ustoichivost po vektornomu kriteriyu i ogranicheniyam vektornoi tselochislennoi zadachi kvadratichnogo programmirovaniya”, Kibernetika i sistemnyi analiz, 2006, no. 5, 63–72 | MR | Zbl

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

[16] Sergienko I. V., Shilo V. P., Zadachi diskretnoi optimizatsii. Problemy, metody resheniya, issledovaniya, Naukova dumka, Kiev, 2003

[17] Sotskov Yu. N., “Issledovanie ustoichivosti optimalnykh raspisanii”, Informatika, 2004, no. 4, 65–75

[18] Sotskov Yu. N., Sotskova N. Yu., Teoriya raspisanii. Sistemy s neopredelennymi chislovymi parametrami, OIPI NAN Belarusi, Minsk, 2004

[19] Daskin M., Network and discrete location, Wiley, New York, 1995 | MR | Zbl

[20] Emelichev V. A., Girlich E., Nikulin Yu. V., Podkopaev D. P., “Stability and regularization of vector problems of integer linear programming”, Optimization, 51:4 (2002), 645–676 | DOI | MR | Zbl

[21] Emelichev V. A., Gurevsky E. E., “On quasi-stability of the vector Boolean problem of minimizing absolute deviations of linear functions from zero”, Computer Science J. of Moldova, 2006, no. 2, 207–218 | MR | Zbl

[22] Emelichev V. A., Kuzmin K. G., Nikulin Yu. V., “Stability analysis of the Pareto optimal solution for some vector boolean optimization problem”, Optimization, 54:6 (2005), 545–561 | DOI | MR

[23] Greenberg H. J., “An annotated bibliography for post-solution analysis in mixed integer and combinatorial optimization”, Advances in computational and stochastic optimization, logic programming and heuristic search, Kluwer Academic Publishers, Boston, MA, 1998, 97–148 | MR

[24] Smale S., “Global analysis and economics, V. Pareto theory with constraints”, J. Math. Econom., 1:3 (1974), 213–221 | DOI | MR | Zbl

[25] Sotskov Yu. N., Leontev V. K., Gordeev E. N., “Some concepts of stability analysis in combinatorial optimization”, Discrete Appl. Math., 58:2 (1995), 169–190 | DOI | MR | Zbl