Geodesic
Decomposition of the problem of approximating the Edgeworth–Pareto hull
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1681-1693 
A. V. Lotov. Decomposition of the problem of approximating the Edgeworth–Pareto hull. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1681-1693. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For nonlinear block separable multicriteria optimization (MCO) problems, a decomposition method is proposed that simplifies the approximation of the Edgeworth–Pareto hull (EPH), i.e., the maximum (by inclusion) set having the same Pareto frontier as the set of feasible criteria vectors in the MCO problem. A two-level system is considered that consists of an upper coordinating level and lower-level subsystems interacting via the upper level. It is assumed that the criteria are related to the upper-level variables. According to the method, preliminarily constructed approximations to block EPHs are used to obtain an EPH approximation for the whole MCO problem. As an example, the EPH for an MCO problem arising in estimating the potential possibilities of water resource management for a cascade of reservoirs is constructed.

[1] Krasnoschekov P. S., Morozov V. V., Popov N. M., Fedorov V. V., “Ierarkhicheskie skhemy proektirovaniya i dekompozitsionnye chislennye metody”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2001, no. 5, 80–89

[2] Haimes Y. Y., Tarvainen K., Shima T., Thadathil J., Hierarchical multiobjective analysis of large-scale systems, Hemisphere Publishing, New York, 1990 | MR

[3] Lotov A. V., “Soglasovanie ekonomicheskikh modelei s ispolzovaniem mnozhestv dostizhimosti”, Matematicheskie metody analiza vzaimodeistviya otraslevykh i regionalnykh sistem, Nauka, Novosibirsk, 1983, 36–44

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

[5] Lotov A. V., Pospelova I. I., Mnogokriterialnye zadachi prinyatiya reshenii, izd. Maks Press, M., 2008, 197 pp.

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

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

[8] Sawaragi Y., Nakayama H., Tanino T., Theory of multiobjective optimization, Acad. Press, Orlando, 1985 | MR | Zbl

[9] Kamenev G. K., Optimalnye adaptivnye metody poliedralnoi approksimatsii vypuklykh tel, Izd. VTs RAN, M., 2007, 233 pp. | MR

[10] Lotov A. V., Maiskaya T. S., “Neadaptivnye metody poliedralnoi approksimatsii obolochki Edzhvorta–Pareto, ispolzuyuschie suboptimalnye metricheskie seti na sfere napravlenii”, Zh. vychisl. matem. i matem. fiz., 52:1 (2012), 35–47 | MR | Zbl

[11] Evtushenko Yu. G., Posypkin M. A., “Metod neravnomernykh pokrytii dlya resheniya zadach mnogokriterialnoi optimizatsii s garantirovannoi tochnostyu”, Zh. vychisl. matem. i matem. fiz., 53:2 (2013), 209–224 | DOI | Zbl

[12] Lotov A. V., Kamenev G. K., Berezkin V. E., “Approksimatsiya i vizualizatsiya paretovoi granitsy dlya nevypuklykh mnogokriterialnykh zadach”, Dokl. AN, 386:6 (2002), 738–741 | MR | Zbl

[13] Berezkin V. E., Kamenev G. K., Lotov A. V., “Gibridnye adaptivnye metody approksimatsii nevypukloi mnogomernoi paretovoi granitsy”, Zh. vychisl. matem. i matem. fiz., 46:11 (2006), 2009–2023 | MR

[14] Lotov A. V., Ryabikov A. I., “Mnogokriterialnyi sintez optimalnogo upravleniya i ego primenenie pri postroenii pravil upravleniya kaskadom gidroelektrostantsii”, Tr. In-ta Matem. i Mekhan. UrO RAN, 20, no. 4, 2014, 187–203 | MR

[15] Kamenev G. K., “Issledovanie skhodimosti i effektivnosti dvukhfaznykh metodov approksimatsii Obolochki Edzhvorta–Pareto”, Zh. vychisl. matem. i matem. fiz., 53:4 (2013), 507–519 | DOI | MR | Zbl

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

[17] Miettinen K., Nonlinear multiobjective optimization, Kluwer, Boston, 1999 | MR | Zbl

[18] Deb K., Multi-objective optimization using evolutionary algorithms, Wiley, Chichester, UK, 2001 | MR | Zbl

[19] Lotov A. V., O tselostnom rassmotrenii ekologo-ekonomicheskikh problem, VTs RAN, M., 1994, 35 pp.

[20] Lotov A., “Computer-based support for planning and negotiation on environmental rehabilitation of water resource systems”, Rehabilitation of Degraded Rivers: Challenges, Issues and Experiences, ed. D. P. Loucks, Kluwer Academic Publishers, 1998, 417–446 | DOI

[21] Lotov A. V., Bourmistrova L. V., Efremov R. V., Bushenkov V. A., Buber A. L., Brainin N. A., “Experience of model integration and Pareto frontier visualization in the search for preferable water quality strategies”, Environmental Modelling and Software, 20:2 (2005), 243–260 | DOI | MR

[22] Sobol I. M., Statnikov R. B., Vybor optimalnykh parametrov v zadachakh so mnogimi kriteriyami, Nauka, M., 1981, 182 pp.

[23] Kamenev G. K., Kondratev D. L., “Ob odnom metode issledovaniya nezamknutykh nelineinykh modelei”, Matem. modelirovanie, 1992, no. 3, 105–118

[24] Lotov A. V., Ryabikov A. I., Buber A. L., “Vizualizatsiya granitsy Pareto pri razrabotke pravil upravleniya GES”, Iskusstvennyi intellekt i prinyatie reshenii, 2013, no. 1, 70–83 | MR

[25] Metodicheskie ukazaniya po razrabotke pravil ispolzovaniya vodokhranilisch, Utverzhdeny prikazom Minprirody Rossii ot 26 yanvarya 2011 g., No 17, http://img.rg.ru/pril/76/46/95/20655.doc