Geodesic
Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 2, pp. 209-224 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The nonuniform covering method is applied to multicriteria optimization problems. The $\varepsilon$-Pareto set is defined, and its properties are examined. An algorithm for constructing an $\varepsilon$-Pareto set with guaranteed accuracy $\varepsilon$ is described. The efficiency of implementing this approach is discussed, and numerical results are presented. 
@article{ZVMMF_2013_53_2_a3,
     author = {Yu. G. Evtushenko and M. A. Posypkin},
     title = {Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {209--224},
     year = {2013},
     volume = {53},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_2_a3/}
}
TY  - JOUR
AU  - Yu. G. Evtushenko
AU  - M. A. Posypkin
TI  - Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 209
EP  - 224
VL  - 53
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_2_a3/
LA  - ru
ID  - ZVMMF_2013_53_2_a3
ER  - 
%0 Journal Article
%A Yu. G. Evtushenko
%A M. A. Posypkin
%T Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 209-224
%V 53
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_2_a3/
%G ru
%F ZVMMF_2013_53_2_a3
Yu. G. Evtushenko; M. A. Posypkin. Nonuniform covering method as applied to multicriteria optimization problems with guaranteed accuracy. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 2, pp. 209-224. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_2_a3/

[1] Podinovskii V. V., Nogin V. D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, Fizmatlit, M., 2007

[2] Shtoier R., Mnogokriterialnaya optimizatsiya, Radio i svyaz, M., 1992 | MR

[3] Lotov A. V., Pospelova I. I., Mnogokriterialnye zadachi prinyatiya reshenii, Maks Press, M., 2008

[4] Branke J., Deb K., Miettinen K., Slowinski R. (Eds.), Multi-objective optimization — interactive and evolutionary approaches, Springer LNCS, 5252, 2008, 470 pp. | Zbl

[5] Gass S., Saaty T., “Parametric objective function, II”, Operations Research, 3 (1955), 316–319 | DOI | MR

[6] Krasnoschekov P. S., Morozov V. V., Fedorov V. V., “Dekompozitsiya v zadachakh proektirovaniya”, Izv. AN SSSR. Ser. Tekhn. Kibernetika, 1979, no. 2, 7–17

[7] Lotov A. V., Bushenkov V. A., Kamenev G. K., Chernykh O. L., Kompyuter i poisk kompromissa. Metod dostizhimykh tselei, Nauka, M., 1997

[8] Evtushenko Yu. G., Potapov M. A., “Metody chislennogo resheniya mnogokriterialnykh zadach”, Dokl. AN SSSR, 291:1 (1986), 25–39 | MR

[9] Lotov A. V., Bushenkov V. A., Kamenev G. K., Interactive decision maps. Approximation and visualization of Pareto Frontier, Kluwer, Boston, 2004 | MR | Zbl

[10] Lotov A., Berezkin V., Kamenev G., Miettinen K., “Optimal control of cooling process in continuous casting of steel using a visualization-based multi-criteria approach”, Appl. Math. Modelling, 29:7 (2005), 653–672 | DOI | Zbl

[11] Zhadan V. G., “Metod parametrizatsii tselevykh funktsii v uslovnoi mnogokriterialnoi optimizatsii”, Zh. vychisl. matem. i matem. fiz., 26:2 (1986), 77–189 | MR

[12] Zhadan V. G., “Metod modifitsirovannoi funktsii Lagranzha dlya zadach mnogokriterialnoi optimizatsii”, Zh. vychisl. matem. i matem. fiz., 28:11 (1988), 1603–1618 | MR | Zbl

[13] Antipin A. S., Golikov A. I., Khoroshilova E. V., “Funktsiya chuvstvitelnosti, ee svoistva i prilozheniya”, Zh. vychisl. matem. i matem. fiz., 51:12 (2011), 2126–2142 | MR | Zbl

[14] Karpenko A. P., Moor D. A., Mukhlisulina D. T., “Multicriteria optimization based on neural network, fuzzy and neuro-fuzzy approximation of decision marker's utility function”, Optical Memory and Neural Networks (Informatin Optics), 21:1 (2012), 1–10 | DOI

[15] Evtushenko Yu. G., “Chislennyi metod poiska globalnogo ekstremuma funktsii (perebor na neravnomernoi setke)”, Zh. vychisl. matem. i matem. fiz., 11:6 (1971), 1390–1403 | Zbl

[16] Evtushenko Yu. G., Ratkin V. A., “Metod polovinnykh delenii dlya globalnoi optimizatsii funktsii mnogikh peremennykh”, Tekhn. kibernetika, 1987, no. 1, 119–127 | MR | Zbl

[17] Evtushenko Yu. G., Malkova V. U., Stanevichyus A. A., “Rasparallelivanie protsessa poiska globalnogo ekstremuma”, Avtomatika i telemekhan., 2007, no. 5, 46–58 | MR | Zbl

[18] Evtushenko Y., Posypkin M., Sigal I., “A framework for parallel large-scale global optimization”, Computer Science — Research and Development, 23:3 (2009), 211–215 | DOI

[19] Evtushenko Yu. G., Posypkin M. A., “Varianty metoda neravnomernykh pokrytii dlya globalnoi optimizatsii chastichno-tselochislennykh nelineinykh zadach”, Dokl. AN, 437:2 (2011), 168–172 | MR | Zbl

[20] Evtushenko Yu. G., Posypkin M. A., “Primenenie metoda neravnomernykh pokrytii dlya globalnoi optimizatsii chastichno tselochislennykh nelineinykh zadach”, Zh. vychisl. matem. i matem. fiz., 51:8 (2011), 1376–1389 | MR | Zbl

[21] Karpenko A. P., Seminikhin A. S., Chernaya L. A., “Metod priblizhennogo postroeniya granitsy oblasti dostizhimosti mnogosektsionnogo robota-manipulyatora”, Nauka i obrazovanie, 2011, no. 01 http://technomag.edu.ru/doc/165078.html

[22] Lotov A. V., “Soglasovanie ekonomicheskikh modelei s ispolzovaniem mnozhestv dostizhimosti”, Matem. metody analiza vzaimodeistviya otraslevykh i regionalnykh sistem, eds. E. L. Berlyand, S. B. Barabash, Nauka, Novosibirsk, 1983

[23] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, BKhV-Peterburg, 2004

[24] Zitzler E., Knowles J., Thiele L., “Quality assessment of Pareto set approximations”, Multi-objective optimization interactive and evolutionary approaches, Springer LNCS, 5252, 2008, 373–404

[25] Bleuler S., Laumanns M., Thiele L., Zitzler E., “PISA — a platform and programming language independent interface for siearch algotithms”, Conf. on Evolutionary multi-Criterion Optimization, EMO 2003, LNCS, 2632, eds. C. M. Fonseca et al., Springer, Berlin, 2003, 494–508 | MR | Zbl