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Математичні моделі і методи розв’язання нелінійних задач розміщення геометричних об’єктів: Автореф. дис… д-ра фіз.-мат. наук / М.В. Новожилова, НАН

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IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO I?IAEAI IAOEIIAOAeOAAIIss ?i. A. I. I?aeai?iiai

IIAIAEEEIAA IA?EIA AIEIAeEIE??AIA

OAeE 519.859

IAOAIAOE*I? IIAeAE? ? IAOIAeE ?ICA’ssCAIIss

IAE?I?EIEO CAAeA* ?ICI?UAIIss

AAIIAO?E*IEO IA’?EO?A

01.05.02 – iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

aeieoi?a o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a – 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a ?inoeooo? i?iaeai iaoeiiaoaeoaaiiy ?i. A.I.
I?aeai?iiai IAI Oe?a?ie.

Iaoeiaee eiinoeueoaio: /eai – ei?aniiiaeaio IAI Oe?a?ie, aeieoi?
oaoi?/ieo iaoe, i?ioani? Noiyi TH??e A?eai?iae/, ?inoeooo

i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie (i.Oa?e?a),
caa?aeoaa/ a?aeae?eo iaoaiaoe/iiai iiaeaethaaiiy ? iioeiaeueiiai
i?iaeooaaiiy.

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?
E?naeueiaa Ieaia Ieoaee?aia, Aei?i?iiao?ianueeee aea?aeaaiee
oi?aa?neoao, caa?aeoaa/ eaoaae?e ia/enethaaeueii? iaoaiaoeee ?
iaoaiaoe/ii? e?aa?iaoeee;

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Eeoaei Ieaa Ieeieaeiae/,
Oe?a?inueea ?iaeaia?ii-iaaeaaia?/ia aeaaeai?y (i. Oa?e?a), caa?aeoaa/
eaoaae?e i?eeeaaeii? iaoaiaoeee

aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? ?iaoeue Ieaa Ieaen?eiae/,
Iieoaanueeee aea?aeaaiee oaoi?/iee oi?aa?neoao ?i. TH.Eiiae?aothea,
caa?aeoaa/ eaoaae?e i?eeeaaeii? iaoaiaoeee ? iaoaiaoe/iiai
iiaeaethaaiiy.

I?ia?aeia onoaiiaa: ?inoeooo e?aa?iaoeee ?i. A.I.Aeooeiaa IAI Oe?a?ie,

a?aeae?e iaoiae?a ?ica’ycaiiy neeaaeieo caaea/ iioei?caoe??, i. Ee?a.

Caoeno a?aeaoaeaoueny “25” eenoiiaaea 1999 ?. i 14 aiaeei? ia
can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.180.01 a ?inoeooo?
i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie ca aae?anith

310046, i. Oa?e?a, aoe. Aei. Iiaea?nueeiai, 2/10.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? ?inoeoooo i?iaeai
iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie ca aae?anith

310046, i. Oa?e?a, aoe. Aei. Iiaea?nueeiai, 2/10.

Aaoi?aoa?ao ?ic?neaiee “23” aeiaoiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee A.I.Caeoeaa

CAAAEUeIA OA?AEOA?ENOENOEEA ?IAIOE

Aeooaeuei?noue oaie. A aaaaoueio aaeocyo ethaenueei? ae?yeueiino?
aeieeathoue caaea/?, iia’ycai? c iioei?caoe??th no?oeoo?e ?
ooieoe?iioaaiiy aaaaoiia?aiao?e/ieo nenoai, o yeeo cae?enith?oueny
noi?nia ia?iaea neeaaeii? aaiiao?e/ii?, aiae?oe/ii? ? eia?/ii?
?ioi?iaoe?? c iaoith aeinyaiaiiy noaio iioeiaeueiiai ooieoe?iioaaiiy.

Iaeiei ?c iniiaieo ?ino?oiaio?a aea/aiiy ? iioei?caoe?? oaeeo nenoai ?
oai??y aeine?aeaeaiiy iia?aoe?e, cie?aia, iiaeae? ? iaoiaee
iaoaiaoe/iiai i?ia?aioaaiiy. A inoaii? aeanyoe??//y aia?ao iaoaiaoe/iiai
i?ia?aioaaiiy ye can?a aeai?o iioeiaeueii? eiio?ao?aoe?? aai iiiaeeie
ia?aiao??a aeey aeinyaiaiiy iaaii? iaoe ae?noaa iiaeaeueoee nooo?aee
?icaeoie cia/iith i??ith caaaeyee ooiaeaiaioaeueiei ?iaioai oaeeo
a?aeiieo oe?a?inueeeo o/aieo, ye aeaaeai?e Ieoaeaae/ A.N., aeaaeai?e IAI
Oe?a?ie Na?a??iei ?.A., aeaaeai?e IAI Oe?a?ie Oi? I.C., aeaaeai?e IAI
Oe?a?ie ?aa/ia A.E., aeaaeai?e IAI Oe?a?ie Ioaie/iee A.I.,
/eai-ei?aniiiaeaio IAI Oe?a?ie Aoaeee A.I., aeaaeai?e IAI Oe?a?ie
??iieue?a TH.I., /eai-ei?aniiiaeaio IAI Oe?a?ie Noiyi TH.A., i?ioani?
E?naeueiaa I.I. oa ?io?.

Iiiaeeia iioei?caoe?eieo caaea/, ui iia’ycai? c oe?eani?yiiaaiei
ia?aoai?aiiyi aaiiao?e/ii? ?ioi?iaoe?? ca?aeii c aeayeei e?eoa???i
iioeiaeueiino?, neeaaea? i?aaeiao oai??? aaiiao?e/iiai i?iaeooaaiiy.

Caaea/? aaiiao?e/iiai i?iaeooaaiiy aeieeathoue o ??ciiiai?oieo aaeocyo
iaoee ? oaoi?ee. Iaeaea an? aiie iia’ycai? c ia?iaeith aaiiao?e/ii?
?ioi?iaoe?? a o?e ?? /anoei?, aea eaeaoueny i?i ?ici?uaiiy aaiiao?e/ieo
ia’?eo?a aeia?eueii? i?inoi?iai? oi?ie, ? iieyaathoue o iiooeo
iioeiaeueiiai ?ici?uaiiy ne?i/aii? iiiaeeie aaiiao?e/ieo ia’?eo?a, ui
aecia/a?oueny aaeoi?ii ia?aiao??a ?ici?uaiiy ia’?eo?a, a caaeaieo
iaeanoyo ?ici?uaiiy i?e iayaiino? ??ciiiai?oieo iaiaaeaiue ? aeayeeo
e?eoa???a yeino? ?ici?uaiiy.

Noai?aiiy oai??? aaiiao?e/iiai i?iaeooaaiiy, iniiaith yei? ? iiaoaeiaa
? aeine?aeaeaiiy ??cieo aeae?a a?aeia?aaeaiue aaiiao?e/ii? ?ioi?iaoe??,
aeicaieeei iiaoaeoaaoe ?aeeio iaoaiaoe/io iiaeaeue oaeeo aaaeeeaeo
i?eeeaaeieo caaea/, ye caaea/? iioeiaeueiiai ?ice?ith i?iieneiaeo
iaoa??ae?a, caaea/? ?aoe?iiaeueiiai aeei?enoaiiy a?aeoiae?a, caaea/?
?ici?uaiiy iaeaaeiaiiy c o?aooaaiiyi iaiaaeaiue iae??ciiiai?oi?oiai
aeaeyaeo, caaea/? ?ici?uaiiy iiaeoe?a ia ?aae?iaeaeo?iii?e ieao?,
caaea/? oi?aae?iiy neeaaeieie oaoi?/ieie nenoaiaie, ?ic?iaea
aaia?aeueieo ieai?a i?iieneiaeo i?aei?e?inoa, i?iaeooaaiiy neeaaeieo
oaoi?/ieo nenoai c o?aooaaiiyi o?ceei-iaoai?/ieo iie?a ??ciiiai?oii?
i?e?iaee, yeui iin?? oeeo iie?a iathoue aeia?eueio i?inoi?iao oi?io
oiui. Aei caaea/? i?yiieooiiai ?ici?uaiiy caiaeyoueny aeaye? caaea/?
oai??? ?iceeaae?a ? ia’?iii-eaeaiaea?iiai ieaioaaiiy. Eean
iioei?caoe?eieo caaea/, iia’ycaieo c ia?aoai?aiiyi aaiiao?e/ii?
?ioi?iaoe??, i?noeoue oaeiae oae? caaea/?, ye caaea/? iie?eooy, caaea/?
?icaeooy aeayei? iiiaeeie ia i?aeiiiaeeie, ui iaia?aoeiathoueny oiui.

A inoaii? o?e aeanyoe??//y i?iaiaeyoueny ?ioaineai? iaoeia?
aeine?aeaeaiiy a aeai?e aaeoc? ciaiue, ui iiynith?oueny ye
neeaaei?noth iiaeaethaaiiy ? iiaoaeiae iaoiae?a ?ica’ycoaaiiy
iioei?caoe?eieo caaea/ aaiiao?e/iiai i?iaeooaaiiy, oae ? iaaecae/aeii
oe?ieei niaeo?ii i?aeoe/ieo canoinoaaiue.

Aeey oni?oiiai ?ica’ycaiiy iaoeiaeo ? i?aeoe/ieo caaea/, ui aeieeathoue
a i?ioean? ia?iaee ? iioei?caoe?? aaeeeeo ianya?a aaiiao?e/ii?
?ioi?iaoe??, iaiao?aei? ia o?eueee ?ic?iaea caaaeueieo i?eioeei?a
iiaeaethaaiiy caaea/ ?aaoey?iiai ? ia?aaoey?iiai ?ici?uaiiy aaiiao?e/ieo
ia’?eo?a, aea ? iiaoaeiaa ? aeine?aeaeaiiy i?iaeaiii-i???ioiaaieo
iaoaiaoe/ieo iiaeaeae eiie?aoieo eean?a caaea/ aeaii? i?aaeiaoii?
iaeano?, iaoiae?a ? aeai?eoi?a ?oiueiai ?ica’ycaiiy.

Eiioeaiooaeueiith caaea/ath ? iaoaiaoe/ia iiaeaethaaiiy iaiaaeaiue (ye
aaiiao?e/ieo, iia’ycaieo c o?aooaaiiyi i?inoi?iai? oi?ie ia’?eo?a, ui
?ici?uothoueny, ? iaeano? ?ici?uaiiy, oae ? iaiaaeaiue, ui iaoiiaeai?
oaoiieia??th i?ioeano, ui iiaeaeth?oueny), ye? aeae?eythoue iaeanoue
i?eionoeieo ?ica’yce?a iioei?caoe?eii? caaea/? aaiiao?e/iiai
i?iaeooaaiiy, ui ?icaeyaea?oueny.

I?e oeueiio iaei??th c iaea?eueo aeooaeueieo caaea/ ? i?i?i?caoe?y
ianyao aiae?oe/ii? ? eia?/ii? ?ioi?iaoe??, yea iio??aia aeey
aaeaeaaoiiai iieno ?aaeueiiai i?ioeano.

Neeaaei?noue aiae?oe/iiai iiaeaiiy iaeano? i?eionoeieo ?ica’yce?a ?
ooieoe?? iaoe caaea/ iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy,
aaaaoiaei??i?noue oa aaaaoiaeno?aiaeuei?noue caaea/, iae?i?ei?noue ?
iaaeeoa?aioe?eiaai?noue a caaaeueiiio aeiaaeeo ooieoe?e iaiaaeaiue
iaeano? i?eionoeieo ?ica’yce?a aeaiaeeoue aeaiee eean caaea/ ca ?aiee
eeane/ii? oai??? aeine?aeaeaiiy iia?aoe?e, oiio aeoaea aeooaeueiith ?
caaea/a noai?aiiy iaoiaeieia?? ?ica’ycaiiy caaea/ aaiiao?e/iiai
i?iaeooaaiiy.

A ca’yceo c oeei aaeeea iaoeiaa cia/aiiy iaaoaa? aeyaeaiiy caaaeueieo
caeiiii??iinoae iiaeaethaaiiy iioei?caoe?eieo caaea/ aaiiao?e/iiai
i?iaeooaaiiy, ui iia’ycaia c caaacia/aiiyi iiaeeeaino? canoinoaaiiy
iaoiae?a ?ica’ycaiiy iaeiiai eeano caaea/ aei ?ioiai, a?aei?iiiai ca
nai?th iaoi?iaeueiith iinoaiiaeith.

Iaea?eueoo neeaaei?noue c iaoaiaoe/ii? oi/ee ci?o i?aaenoaaey? eean
iioei?caoe?eieo caaea/ ia?aaoey?iiai ?ici?uaiiy ia’?eo?a aeia?eueii?
i?inoi?iai? oi?ie, na?aae yeeo iaeiaio aea/aieie ? caaea/? ia?aaoey?iiai
?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia’?eo?a (oiaoi ia’?eo?a,
iieiaeaiiy yeeo a iaeano? ?ici?uaiiy oa?aeoa?eco?oueny ia o?eueee
ia?aiao?aie o?aineyoe??, aea ? eooii iiai?ioo aeanieo nenoai eii?aeeiao)
a ?cio?iiieo ? ai?cio?iiieo iaeanoyo aeia?eueii? i?inoi?iai? oi?ie c?
ci?iieie iao?e/ieie oa?aeoa?enoeeaie. A?aenooi? aoaeoeai? caniae
?ica’ycaiiy oaeeo caaea/.

Ioaea, iiaeaethaaiiy oa ?ica’ycaiiy iioei?caoe?eieo caaea/
ia?aaoey?iiai ?ici?uaiiy ia’?eo?a aeia?eueii? i?inoi?iai? oi?ie ia?
caaaeueiioai?aoe/ia cia/aiiy.

Iacaaaeath/e ia oa, ui iioei?caoe?ei? caaea/? aaiiao?e/iiai
i?iaeooaaiiy iaeaaeaoue aei eeano NP-iiaieo caaea/, ? ia?aaaaeia
a?eueo?noue iaoiaeee ?ica’ycaiiy icia/aieo eean?a caaea/ ? aa?enoe/ieie,
oaeaeeee ?icaeoie ia/enethaaeueii? oaoi?ee iaaea? iiaeeea?noue
/enaeueii? ?aae?caoe?? caaea/ i?aeoe/ii? aei??iino?, oiio ? aeooaeueiei
i?iaeiaaeaiiy aeine?aeaeaiue o aaeoc? ?ic?iaee cania?a iiooeo
aeiaaeueii-iioeiaeueiiai ?ica’ycaiiy caaea/ ?ici?uaiiy, ui
?icaeyaeathoueny.

Ioaea, caaaeueia oai??y aaiiao?e/iiai i?iaeooaaiiy acaaae? ?
iiaeaethaaiiy ? ?ica’ycaiiy iioei?caoe?eieo caaea/ ia?aaoey?iiai
?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia’?eo?a a ?cio?iiieo ?
ai?cio?iiieo iaeanoyo ?ici?uaiiy cie?aia, iio?aao? iiaeaeueoiai
?icaeoeo, ui ? aecia/eei oaio aeaii? aeena?oaoe?eii? ?iaioe.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie.

Aeena?oaoe?eia ?iaioa aeeiiaia a ia??iae c 1989 ?. ii 1999 ?. o
a?aeae?e? iaoaiaoe/iiai iiaeaethaaiiy ? iioeiaeueiiai i?iaeooaaiiy
?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A. I. I?aeai?iiai IAI Oe?a?ie ? ?
/anoeiith aeine?aeaeaiue, ui aeeiiothoueny i?ae ea??aieoeoaii /e.-ei?.
IAI Oe?a?ie TH. A. Noiyia ca?aeii c ieaiaie iaoeiai-aeine?aeieo ?ia?o ca
i?ia?aiaie:

-6.4.1. “?ioaa?iaai? eiii’thoa?i? oaoiieia?? i?iaeooaaiiy” ca ae/a
oaiaie:

–“?ioaa?iaaia eiii’thoa?ia oaoiieia?y aaiiao?e/iiai i?iaeooaaiiy
neeaaeieo oaoi?/ieo nenoai” (1992-1996??., NA?0193E020060);

–“?ioaeaeooaeuei? nenoaie aaiiao?e/iiai i?iaeooaaiiy” (1992-1993 ??., N
A?0193V020061), (Iinoaiiaa AeEIO Oe?a?ie);

-1.12.5 “I?iaeaie aaoiiaoecaoe?? i?iaeooaaiiy oaoi?/ieo nenoai” ca ae/a
oaiaie:

–“Iaoaiaoe/ia iiaeaethaaiiy neeaaeieo oaoi?/ieo nenoai iiaeoeueiiai
oeio”, (1990-1993 ??., N A? 01900009448);

–“?ic?iaea ? aeine?aeaeaiiy ?ioaeaeooaeueii? nenoaie a?aeia?aaeaiiy
aaiiao?e/ii? ?ioi?iaoe?? aeey iioei?caoe?? ? iiaeaethaaiiy
o?ceei-iaoai?/ieo i?ioean?a ? oaoi?/ieo nenoai” (1994 – 1997 ??., N A?
0197V012281);

–1.7.2.2 “?ic?iaea ? aeine?aeaeaiiy iaoaiaoe/ieo iiaeaeae caaea/
iioei?caoe?? ?ici?uaiiy o?eaei??ieo aaiiao?e/ieo ia’?eo?a” (1998-2001
pp.);

— Aeiaiai?o c AeEIO Oe?a?ie (oiiae ooiaeaiaioaeueieo aeine?aeaeaiue) ?
12.3/66 “?ic?iaea iiaeo iaoiae?a ni?eueiiai caa?aaeaiiy oa ia?aoai?aiiy
neeaaeii? aiae?oe/ii? oa aaiiao?e/ii? ?ioi?iaoe?? a iaoaiaoe/iiio ?
eiii’thoa?iiio iiaeaethaaii?”, (1994 – 1997 ??.).

— Aeiaiai?o c I?i?noa?noaii o ni?aaao iaoee ? oaoiieia?e Oe?a?ie N
2/847-97 “Aiaeioeei-aaiiao?e/ia oa eiii’thoa?ia iiaeaethaaiiy aenieeo
oaoiieia?e aeaioiaeaiiy oa aenieoaoaoe?? ia’?eo?a neeaaeii?
eiio?ao?aoe??, ui i?aeaeathoueny aenoeia?aaeiaioiei aieeaai”.

Iaoith ?iaioe ? ?ic?iaea iaoiaeieia?? iaoaiaoe/iiai ? eiii’thoa?iiai
iiaeaethaaiiy ia?aaoey?iiai ?ici?uaiiy aeaiaei??ieo ? o?eaei??ieo
aaiiao?e/ieo ia’?eo?a c o?aooaaiiyi iiaeeeaino? ?o iiai?ioo a iaeanoyo
aeia?eueii? i?inoi?iai? oi?ie c? ci?iieie iao?e/ieie oa?aeoa?enoeeaie ?
noai?aiiy iiaeo cania?a ?ica’ycaiiy eeano iioei?caoe?eieo caaea/
aaiiao?e/iiai i?iaeooaaiiy, ui ?icaeyaea?oueny.

O aeena?oaoe?? aeey aeinyaiaiiy oe??? iaoe iinoaaeai? ianooii? iniiai?
iaoeia? caaaeaiiy:

1.Ia iniia? aiae?co ?nioth/eo cania?a oi?iae?caoe?? iniiaieo iaiaaeaiue
caaea/? ia?aaoey?iiai ?ici?uaiiy ia’?eo?a ?ic?iaeoe aia?ao
oi?iae?caoe?? oiia aca?iiiai iaia?aoeio a caaaeueiiio aeiaaeeo
iai???ioiaaieo aaiiao?e/ieo ia’?eo?a oa oiia ?o ?ici?uaiiy o iaeano?
?ici?uaiiy aeey ia’?eo?a ? iaeanoae aeia?eueii? i?inoi?iai? oi?ie c?
ci?iieie aaiiao?e/ieie oa?aeoa?enoeeaie.

2. Aeoiaey/e c iaoaiaoe/ii? iiaeae? iniiaii? caaea/? ia?aaoey?iiai
?ici?uaiiy ia’?eo?a, aiae?co ?nioth/eo cania?a ?ica’ycaiiy caaea/ c
eeano, ui ?icaeyaea?oueny, ?ic?iaeoe iaoiaeieia?th iiooeo ?ica’ycaiiy
iniiaii? caaea/?. Ia iniia? cai?iiiiiaaieo iaoiae?a noai?eoe
aeai?eoi?/ia ? i?ia?aiia caaacia/aiiy eeano caaea/ ia?aaoey?iiai
?ici?uaiiy ia’?eo?a a iaeanoyo aeia?eueii? i?inoi?iai? oi?ie.

3. I?iaiae?coaaoe iaoiaee ? aeai?eoie c oi/ee ci?o ?oiuei?
ia/enethaaeueii? neeaaeiino?.

4. ?ic?iaeoe ? aeine?aeeoe i?iaeaiii-i???ioiaai? iaoaiaoe/i? iiaeae?
caaea/ aaiiao?e/iiai i?iaeooaaiiy, aeae?eeoe ?oi? nooo?a? iniaeeaino?,
aeine?aeeoe iaeanoue i?eionoeieo ?ica’yce?a eean?a caaea/, ui
?icaeyaeathoueny.

Iniiai? iia? iaoeia? ?acoeueoaoe:

1. Ae?noaa iiaeaeueoee ?icaeoie aia?ao oi?iae?caoe?? oiia ?ici?uaiiy
ia’?eo?a a ?cio?iiieo ? ai?cio?iiieo iaeanoyo aeia?eueii? i?inoi?iai?
oi?ie o R2, iniiaaiee ia iiiyoo? F-ooieoe?? ia?e ia’?eo?a.

2. Iaea?aeaii iia? caniae aiae?oe/iiai iieno F-ooieoe?? i???ioiaaieo oa
iai???ioiaaieo ia’?eo?a, iia? aeanoeaino? F-ooieoe??.

3. Aeine?aeaeaii iaeanoue i?eionoeieo ?ica’yce?a caaea/? ?ici?uaiiy
iai???ioiaaieo aaaaoieooiee?a o iaeano? ?ici?uaiiy neeaaeii? i?inoi?iai?
oi?ie c? ci?iieie iao?e/ieie oa?aeoa?enoeeaie, aeae?eai? iia? nooo?a?
eiino?oeoeai? iniaeeaino? iaeano? i?eionoeieo ?ica’yce?a.

4. Aia?oa canoiniaaii aia?ao F-ooieoe?e aeey iieno oiia aca?iiiai
?ici?uaiiy aeaio iai???ioiaaieo aaaaoia?aiiee?a o R3.

5. Iiaoaeiaaii iia? oi/i? ? iaaeeaeai? caniae ?ica’ycaiiy iiaeo eean?a
iioei?caoe?eieo caaea/ ?ici?uaiiy o iaeanoyo ?ici?uaiiy c? ci?iieie
iao?e/ieie oa?aeoa?enoeeaie.

6. Ae?noaa iiaeaeueoee ?icaeoie iaoiae ?ica’ycaiiy eiia?iaoi?ii?
caaea/? ?ici?uaiiy i?yiieooiee?a ia iniia? canoinoaaiiy cania?a
iaia?a?aii? iioei?caoe??, a naia – cania?a aeoeaiiai iaai?o.
Iaoiaeieia?y ?ica’ycaiiy aeaiaei??ii? caaea/? i?yiieooiiai ?ici?uaiiy
canoiniaaia aei iiaiai eeano caaea/ – caaea/? iaeoaaiiy
a?ia?ia?aeaeai?iaae?a.

7. ?ic?iaeaii iiaee iaoiae ?ica’ycaiiy caaea/? ?ici?uaiiy
iai???ioiaaieo aaaaoieooiee?a, yeee iniiaaii ia iioei?caoe?? ca a?oiaie
ia?aiao??a o?aineyoe?? ia’?eo?a ? eooiaeo ia?aiao??a ?ici?uaiiy ? ui
a?aoiao? aaiiao?e/i? iniaeeaino? iaeano? i?eionoeieo ?ica’yce?a caaea/?.

8. ?ic?iaeaii iiaa aeai?eoi?/ia ? i?ia?aiia caaacia/aiiy eeano caaea/
ia?aaoey?iiai ?ici?uaiiy ia’?eo?a a iaeanoyo aeia?eueii? i?inoi?iai?
oi?ie c ioe?ieaie ia/enethaaeueii? neeaaeiino? aeai?eoi?a.

9. Io?eiaee iiaeaeueoee ?icaeoie i?iaeaiii-i???ioiaai? iaoaiaoe/i?
iiaeae? caaea/ aaiiao?e/iiai i?iaeooaaiiy, aeine?aeaeaii ?oi?
iniaeeaino?, ?ic?iaeaii iaoiaeieia?/ia oa i?ia?aiia caaacia/aiiy.

A??ia?aei?noue oa iaa?oioiaai?noue iaea?aeaieo ?acoeueoao?a
aecia/a?oueny aeei?enoaiiyi caaaeueiiaeciaieo cania?a iaoaiaoe/iiai
iiaeaethaaiiy ? aaiiao?e/iiai i?iaeooaaiiy, iaoaiaoe/ii? iiaeae?
iniiaii? caaea/? ia?aaoey?iiai ?ici?uaiiy ia’?eo?a. Aoaeoeai?noue
cai?iiiiiaaieo iaoiae?a, ?o aeai?eoi?/ii? ? i?ia?aiii? ?aae?caoe??
i?aeoaa?aeaeo?oueny aiae?cii ia/enethaaeueii? neeaaeiino? ? ii??aiyiiyi
io?eiaieo ?acoeueoao?a ye ca oaeaeeiae??th, oae ? ca ye?noth ?ica’ycaiiy
c aiaeia?/ieie ?acoeueoaoaie a?o/eciyieo ? ca?oa?aeieo aeine?aeiee?a.

Aaoi?ii ?ic?iaeaiee aaie i?ia?aiieo iiaeoe?a, ui noai?th? i?ia?aiia
caaacia/aiiy aeey ?ica’ycaiiy eeano caaea/ ia?aaoey?iiai ?ici?uaiiy
i???ioiaaieo ? iai???ioiaaieo aaiiao?e/ieo ia’?eo?a. Caaaeueiee ianya
i?ia?ai, ye? ?aae?cothoue iaoaiaoe/iee aia?ao, ui i?iiiio?oueny,
neeaaea? iiiaae 30000 iia?aoi??a.

Oai?aoe/ia cia/aiiy ?iaioe. An? oai?aoe/i? ?acoeueoaoe iiaeai? o
aeaeyae? aecia/aiue, oai?ai, aeanoeainoae, iien?a aeai?eoi?a, ui a
cia/i?e /anoei? i?eaiaeyoueny aia?oa aai ocaaaeueiththoue aaea a?aeii?.

I?aeoe/ia cia/aiiy ?iaioe. Iaoeia? ?acoeueoaoe aeena?oaoe?eii? ?iaioe ?
iiaeaeueoei ?icaeoeii oai??? aaiiao?e/iiai i?iaeooaaiiy, aeicaieythoue
caaaeyee aeae?eaiith caaaeueieo ooiaeaiaioaeueieo iniaeeainoae
iioei?caoe?eieo caaea/ ?ici?uaiiy, ??ciiiai?oieo ca nai?th
iaoi?iaeueiith iinoaiiaeith, ae??oeoe aaaaoi caaea/ aaiiao?e/iiai
i?iaeooaaiiy, ui ?ai?oa ia aoee ?ica’ycai?.

Noeoii?noue ?ic?iaeaieo iaoaiaoe/ieo iiaeaeae, iaoiae?a, aeai?eoi?a ?
i?ia?aiieo eiiieaen?a iiaea aeei?enoiaoaaoeny o aeaeyae?
iioei?caoe?eiiai yae?a a nenoaiao aaoiiaoeciaaiiai i?iaeooaaiiy ea?o
?ice?ith i?iieneiaeo iaoa??ae?a o acooo?a?e, oaenoeeuei?e ?
iaoaeiia?iai?e i?iieneiaino?, i?e noai?aii? ?ano?nicaa??aath/eo
oaoiieia?e, ye? aeicaieyoue i?aeiyoe aoaeoeai?noue aeei?enoaiiy
?ano?n?a. Inoaii?e oaeo iaaoaa? iniaeeaiai cia/aiiy a oiiaao aei?noeeo
iaiaaeaiue o?iainiaeo ? aia?aaoe/ieo ?ano?n?a a iao?e e?a?i?. E??i oiai,
?ic?iaeai? iaoiaee ? aeai?eoie iiaeooue aooe canoiniaai? i?e
i?iaeooaaii? a?aen?e?a o?ainii?oieo cania?a, aaia?aeueieo ieai?a
i?aei?e?inoa oiui.

Iaoaiaoe/ia, aeai?eoi?/ia ? i?ia?aiia caaacia/aiiy eeano caaea/
ia?aaoey?iiai ?ici?uaiiy ia’?eo?a iiaea aeei?enoiaoaaoeny a iaoeiaeo
aeine?aeaeaiiyo aeey oi?iae?caoe?? oiia ?ici?uaiiy a iaeanoyo
aeia?eueii? i?inoi?iai? oi?ie c? ci?iieie iao?e/ieie oa?aeoa?enoeeaie,
aeey ciaoiaeaeaiiy eieaeueii-iioeiaeueieo ? aeiaaeueii-iioeiaeueieo
?ica’yce?a a?aeiia?aeieo caaea/ ?ici?uaiiy.

Ie?ai? aeai?eoie ? i?ia?aie iiaeooue aeei?enoiaoaaoeny i?e ia?iaoe?
?ioi?iaoe?? a aeieia?/ieo caaea/ao ? a caaea/ao iii?oi?eiao Caie?.

?aae?caoe?y ? ai?iaaaeaeaiiy. Iiaeae?, iaoiaee, aeai?eoie oa i?ia?aiia
caaacia/aiiy caaea/ iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy, ui
?icaeyaeathoueny o aeena?oaoe?ei?e ?iaio?, aoei aeei?enoaii o iaoeiaeo
aeine?aeaeaiiyo ?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A. I. I?aeai?iiai
IAI Oe?a?ie i?ae /an aeeiiaiiy aea?aeathaeaeaoieo oai ? aeiaiai??a c
AeEIO Oe?a?ie (oiiae ooiaeaiaioaeueieo aeine?aeaeaiue) ? c I?i?noa?noaii
o ni?aaao iaoee ? oaoiieia?e Oe?a?ie a ia??iae c 1991 ?. ii oaia??oi?e
/an.

Iniiai? caniae iaoaiaoe/iiai iiaeaethaaiiy, cai?iiiiiaai?
iaoiaee

?ica’ycaiiy caaea/ iioei?caoe?eiiai aaiiao?e/iiai i?iaeooaaiiy
ai?iaaaeaeai? aei iaa/aeueiiai i?ioeano Oa?e?anueeiai aea?aeaaiiai
oaoi?/iiai oi?aa?neoaoo aoae?aieoeoaa ? a?o?oaeoo?e i?ae /an i?aeaioiaee
oa aeeeaaeaiiy oaeeo eaeoe?eieo eo?n?a: “Oaoi?/i? caniae a
a?o?oaeoo?iiio i?iaeooaaii?“, “Aeene?aoiee aiae?c“, “Iaoiaee
aeine?aeaeaiiy iia?aoe?e“ (1997-1999 ??.).

Ai?iaaoe?y ?acoeueoao?a aeine?aeaeaiiy. Iniiai? ?acoeueoaoe ?iaioe
aeiiia?aeaeeny oa io?eiaee noaaeaiiy ia: 18 i?aeia?iaeieo oa
iaoe?iiaeueieo eiioa?aioe?yo oa e?eueeio iaoeiaeo nai?ia?ao, a naia:

-Ananithciiio nai?ia?? “Iiaeaethaaiiy ?aa?iiaeueieo nenoai” (Ooa, 1990
?.); -Ananithci?e oeie? “Nenoaie i?ia?aiiiai caaacia/aiiy ?ica’yceo
caaea/ iioeiaeueiiai ieaioaaiiy” (Eino?iia, 1990 ?.); I?aeia?iaei?e
eiioa?aioe?? “Mathematical Optimization” (Aa?e?i, I?ia//eia, 1990 ?.);
?anioae?eainuee?e iaoeiai-oaoi?/i?e eiioa?aioe?? “NAI? oaoiieia?/ii? ?
eiino?oeoi?nueei? i?aeaioiaee ae?iaieoeoaa a iaoeiiaoaeoaaii?” (Oa?e?a,
1990 ?.); – Ananithci?e oeie? “Ieoaiiy iioei?caoe?? ia/eneaiue” (E?ei,
1991 ?.); – 12-e Ananithci?e eiioa?aioe?? “Nenoaie i?ia?aiiiai
caaacia/aiiy ?ica’ycaiiy aeiiii?/ieo caaea/” (Ia?aa-Ee?nnoo, 1992 ?.); –
I?aeia?iaei?e oeie? “I?iaeooaaiiy ANE ? ANO neeaaeieie ia’?eoaie”
(Ooaina, ?in?y, 1992 ?.); – 46-e iaoeia?e eiioa?aioe?? i?ioani??a ?
aeeeaaea/?a Iieoaanueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo (Iieoaaa,
1994 ?.); – 17-e I?aeia?iaei?e eiioa?aioe?? “System Modeling and
Optimization” (I?aaa, *ao?y , 1995 ?.); – I?aeia?iaei?e eiioa?aioe??
“Combinatorial Optimization’-96” (Eiiaeii, Aaeeea A?eoai?y, 1996 ?.); –
I?aeia?iaei?e eiioa?aioe?? “Iaoaiaoeea ? ienoaoeoai” (Nocaeaeue, ?in?y,
1996 ?.); – 18th International Conference on Software Engineering
(Aa?e?i, I?ia//eia, 1996 ?.); – I?aeia?iaei?e iaoeiai-oaoi?/i?e
eiioa?aioe?? “I?ia?aneai? oaoiieia?? iaoeiiaoaeoaaiiy ? no/ani?noue”
(Naaanoiiieue, 1996 ?.); – I?aeia?iaei?e eiioa?aioe?? “Cooperation and
Business Opportunities for Eastern/Western European countries in the IT
field” (Aoaeaiaoo, Oai?ueia, 1997 ?.); – 15-e I?aeia?iaei?e eiioa?aioe??
“Iaoaiaoeea. Eiii’thoa?, Ina?oa”, (Iou?ii, ?in?y, 1997 ?.);- 1-io
I?aeia?iaeiiio Oi?oi? “Aeaeo?ii?ea ? iieiaeue a OOI noi??//?” (Oa?e?a,
1997 ?.); – 53-e iaoeiai-i?aeoe/i?e ? iaa/aeueii-iaoiaee/i?e
eiioa?aioe?? i?ioani??a ? aeeeaaea/?a Oa?e?anueeiai aea?aeaaiiai
oi?aa?neoaoo aoae?aieoeoaa ? a?o?oaeoo?e (Oa?e?a, 1998 ?.); – 16th
European Conference on Operational Research (A?thnnaeue, Aaeuea?y, 1998
?.); – iino?eii ae?th/iio nai?ia?? “Iaoaiaoe/i? iaoiaee aaiiao?e/iiai
i?iaeooaaiiy” (Oa?e?a, 1991-1999 ??.) i?e iaoeia?e ?aae? ca i?iaeaiith
“E?aa?iaoeea” IAI Oe?a?ie, iaoeiaiio nai?ia?? a?aeae?eo ? 120 ?inoeoooo
e?aa?iaoeee ?i. A. I. Aeooeiaa IAI Oe?a?ie (Ee?a, 1999 ?.).

Ioae?eaoe??. Ca oaiith aeena?oaoe?? iioae?eiaaii 30 iaoeiaeo ?ia?o, a
oiio /ene?: 1 iiiia?ao?y, 17 noaoae o iaoeiaeo aeaeaiiyo (aeo?iaeao oa
ca??ieeao iaoeiaeo i?aoeue), 2 aeaiiiiaaieo ?iaioe, 3 aeiiia?ae? a
iaoa??aeao i?aeia?iaeieo iaoeiaeo eiioa?aioe?e, 5 oac aeiiia?aeae ia
i?aeia?iaeieo ? iaoe?iiaeueieo iaoeiaeo eiioa?aioe?yo, 2 i?ai?eioa
?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A. I. I?aeai?iiai IAI Oe?a?ie.

O 1997 ?ioe? I?aceae?y IAI Oe?a?ie i?enoaeeea aaoi?o i?ai?th
Iaoe?iiaeueii? aeaaeai?? iaoe Oe?a?ie ca na??th e?aueo iaoeiaeo ?ia?o.

Iniaenoee aianie caeiaoaa/a. An? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
iaea?aeai? ca iniaenoith o/anoth aaoi?a. O iiiia?ao?? [1] aaoi?ii
iniaenoi iaienai? ?icae?ee 4.1, 4.2, 4.3.

O i?aoeyo, ui iaienai? o ni?aaaoi?noa?, aeena?oaioo iaeaaeaoue: [2] –
eiioeaioe?y iiaoaeiae nenoaie, ui i???ioiaaia ia ?ica’ycaiiy caaea/
i?yiieooiiai ?ici?uaiiy c iiaeeea?noth iiaeaethaaiiy ??cieo
oaoiieia?/ieo iaiaaeaiue; [6] – aiae?c aeai?eoi?a aioo??oiuei? oi/ee c
oi/ee ci?o ?oiuei? ia/enethaaeueii? neeaaeiino? ? iiaeeeaino?
canoinoaaiiy aei ?ica’ycaiiy caaea/ aaiiao?e/iiai i?iaeooaaiiy; [8] –
iiaeaethaaiiy ? aeine?aeaeaiiy iaeano? i?eionoeieo ?ica’yce?a caaea/?
?ici?uaiiy i???ioiaaieo aaaaoieooiee?a o aaaaoica’yci?e iaeano?
?ici?uaiiy; [9] – iiaoaeiaa iaoaiaoe/ii? iiaeae? iioei?caoe?eii? caaea/?
?ici?uaiiy iai???ioiaaiiai aaaaoia?aiieea o aaaaoia?aiieeo c? ci?iieie
iao?e/ieie oa?aeoa?enoeeaie; [10, 24] – aiae?c aoaeoeaiino? aeai?eoi?a
?ica’ycaiiy iioei?caoe?eieo caaea/ ?ici?uaiiy; [11] – iiaeaethaaiiy
caaea/? iioeiaeueiiai ?ici?uaiiy iai???ioiaaieo aaaaoieooiee?a o
aaaaoica’yci?e iaeano? ?ici?uaiiy ? aeeo/aiiy oiia eieaeueii?
ca?aeiino?; [13] – canoinoaaiiy iiiyooy F-ooieoe?? aei caaea/
aaiiao?e/iiai i?iaeooaaiiy, yeui ia’?eoe ?ici?uaiiy ? i?aea ia
u?eueieie; [14] – iinoaiiaea caaea/? aeine?aeaeaiiy, ?ic?iaea
i?eioeeiiaeo iniia canoinoaaiiy iaoiaeeee iaia?a?aii? iioei?caoe??, a
naia, no?aoaa?? aeoeaiiai iaai?o, aei eiia?iaoi?ii? caaea/? i?yiieooiiai
?ici?uaiiy; [17] – ii??aiyiiy, aiae?c ia/enethaaeueii? neeaaeiino? ?
canoinoaaiiy aeai?eoi?a, ui ?icaeyaeathoueny, aei ?ica’ycaiiy caaea/?
?ici?uaiiy iai???ioiaaieo aaaaoieooiee?a; [18] – canoinoaaiiy no?aoaa??
aeoeaiiai iaai?o aei ia?iaee ?ioi?iaoe?? i?i e?ioeaa? aa?oeie aea?aaa
?ica’yce?a caaea/? i?yiieooiiai ?ici?uaiiy, aeai?eoi?/ia oa i?ia?aiia
?aae?caoe?y; [19] – iiaeaethaaiiy caaea/? ?ici?uaiiy ne?i/aii? iiiaeeie
a?ia?ia?aeaeai?iaae?a o a?ia?ia?aeaeai?iaae?, can?a ?ica’ycaiiy caaea/?;
[20] – iiaeaethaaiiy ? aeine?aeaeaiiy eiino?oeoeaieo aeanoeainoae
iaeano? i?eionoeieo ?ica’yce?a caaea/? ?ici?uaiiy i???ioiaaieo
aaaaoieooiee?a o nioc? c aeaoaeoieie ciiaie; [21, 30] – iiaeaethaaiiy ?
aeine?aeaeaiiy iaeano? i?eionoeieo ?ica’yce?a caaea/? ?ici?uaiiy
iai???ioiaaiiai aaaaoia?aiieea a aaaaoia?aii?e iaeano?; [22] – iiaoaeiaa
iaoiaeo ?ica’ycaiiy, aiae?c iiiaeiee?a Eaa?aiaea c oi/ee ci?o
aaiiao?e/ieo iniaeeainoae caaea/? i?yiieooiiai ?ici?uaiiy; [23, 27] –
aeai?eoi?/ia ? i?ia?aiia ?aae?caoe?y iaoiaeo ?ica’ycaiiy caaea/?, ui
?icaeyaea?oueny; [25] – aeine?aeaeaiiy aeanoeainoae neiao??? iaeano?
i?eionoeieo ?ica’yce?a caaea/? i?yiieooiiai ?ici?uaiiy; [26] –
iiaeaethaaiiy caaea/?, ui ?icaeyaea?oueny, ye caaea/? iioeiaeueiiai
?ici?uaiiy aaaaoieooiee?a o nioc?; [27, 28] – iiaeeo?eaoe?y
no?aoaa?? aeoeaiiai iaai?o aeey ?ica’ycaiiy 2D caaea/ aaiiao?e/iiai
i?iaeooaaiiy.

Caaaeueiee ianya ioae?eaoe?e ca oaiith aeena?oaoe?? neeaaea? iiiaae 6
ae?oeiaaieo a?eoo?a. E??i oiai, a Oe??IOA? ca?a?no?iaaii 4
iaoeiai-oaoi?/ieo ca?oe ca aea?aeathaeaeaoieie oaiaie, ui aeeiiai? ca
oaiith aeena?oaoe?? i?e o/ano? aaoi?a.

No?oeoo?a ? ianya ?iaioe. Aeena?oaoe?y i?noeoue anooi, i’youe
?icae?e?a, ae-

niiaee c ?iaioe, 2 aeiaeaoee, iiaiee ianya aeena?oaoe?? – 281 noi?., c
ieo 251 noi?.

iaoeiiieniiai oaenoo, 71 ?enoiie, 1 oaaeeoey, nienie aeei?enoaieo
aeaea?ae c 204 iaeiaioaaiue ia 20 noi?.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aeooaeuei?noue oaie aeena?oaoe??, iieacaia ??
iaoeiaa ni?yiiaai?noue, noi?ioeueiaaia iaoa ?iaioe oa caaea/?
aeine?aeaeaiiy, ye? iio??aii ae??oeoe aeey ?? aeinyaiaiiy. Iiaeaia
ei?ioea oa?aeoa?enoeea ?acoeueoao?a aeine?aeaeaiiy, nooiaith ?o
ai?iaaoe?? oa iioae?eoaaiiy.

Ia?oee ?icae?e aeena?oaoe?? i?enay/aii aiae?oe/iiio iaeyaeo e?oa?aoo?e
ca oaiith aeena?oaoe?? ? aeai?o iai?yie?a aeine?aeaeaiue.

Aiae?c no/aniiai noaio aeaii? i?iaeaie ca iaoa??aeaie a?o/eciyii? ?
ca?oa?aeii? iaoeiai? i?ane oa aea/aiiy i?aoeue oaeeo a?aeiieo a/aieo o
aaeoc? ?ica’ycaiiy caaea/ ?ici?uaiiy, ye i?io. Iooa/iaa A. I. (?in?y),
i?io. Dowsland W. (Aaeeea A?eoai?y), i?io. J.A.S. Ferreira
(Ii?ooaae?y), i?io. J. Terno (I?ia//eia), i?io. V. Milenkovic (NOA) oa
?i. iieacaee, ui iaea?eueo ?iciianthaeaeaiei niiniaii ? aai iineaaeaiiy
iaiaaeaiue caaea/?, aae aei iiaiiai ?aii?oaaiiy i?inoi?iai? oi?ie
ia’?eo?a, ui ?ici?uothoueny, oeyoii caaaeaiiy caaea/? aei caaea/?
iaeiiaei??iiai ?ici?uaiiy, oiaoi aei caaea/? e?i?eiiai i?ia?aioaaiiy,
aai o?enoaaiiy ia?aiao??a ?ici?uaiiy ia’?eo?a. Aiane?aeie oeueiai
?ica’ycie caaea/? eeoa aeiaaeeiai iiaea aeyaeoeny iioeiaeueiei.
Iaea?eueo aeine?aeaeaieie ? caaea/? e?i?eiiai (iaeiiaei??iiai)
?ici?uaiiy, oa caaea/? a?eueeioeiiiai i?yiieooiiai ?ici?uaiiy. Eiaeia
ie?aia caaea/a ?ici?uaiiy ?icaeyaea?oueny eeoa o eiioaeno? nai??
iaoi?iaeueii? iinoaiiaee. A?ae ooiaeaiaioaeueieo aeine?aeaeaiue a aeai?e
i?aaeiaoi?e iaeano? i?ecaiaeeoue aei oiai, ui iaeaea cian?i ia
?icaeyaeathoueny caaea/? ?ici?uaiiy iai???ioiaaieo aaiiao?e/ieo ia’?eo?a
o aaaaoieooieo ?cio?iiieo oa ai?cio?iiieo iaeanoyo c? ci?iieie
iao?e/ieie oa?aeoa?enoeeaie. A ?iaio? iieacaii, ui oeae iaaeie?e iiaeia
e?ea?aeoaaoe ia iniia? ?aeeiiai i?aeoiaeo, ?aeeii? iaoaiaoe/ii? iiaeae?
caaea/ ?ici?uaiiy, yea ?icaeyaea?oueny a ?aieao oai??? aaiiao?e/iiai
i?iaeooaaiiy ? ?ic?iaey?oueny o iaoeia?e oeie? /eaia-ei?aniiiaeaioa IAI
Oe?a?ie i?ioani?a Noiyia TH.A.

Iniiai? ?acoeueoaoe ?icae?eo iioae?eiaaii a i?aoeyo [8, 6, 7, 21, 23].

O ae?oaiio ?icae?e? aeena?oaoe?? “Noai i?iaeaie ? iinoaiiaea caaea/?
aeine?aeaeaiiy” oi?ioeththoueny iaiaaeaiiy, ye? aeeo/athoue iniiaio aeey
aeaii? aeena?oaoe?eii? ?iaioe caaea/o aeine?aeaeaiiy na?aae an???
iiiaeeie caaea/ aaiiao?e/iiai i?iaeooaaiiy, iaaiaeeoueny iinoaiiaea
iniiaii? caaea/? aeine?aeaeaiiy ye caaea/? ?ici?uaiiy a oa?i?iao
aaiiao?e/ii? ?ioi?iaoe??.

Iioei?caoe?ei? caaea/? aaiiao?e/iiai i?iaeooaaiiy cia/iith i??ith
iia’ycai? c ia?iaeith ei?oaaeo aaiiao?e/ii? ?ioi?iaoe?? g i?i iaaio
oi/eiao iiiaeeio (aaiiao?e/iee ia’?eo) S, yea neeaaea?oueny c o?ueio
eiiiiiaio (o?eniaaieo aai ci?iieo)

g = (s1, s2 ,…,sq , m1 ,…,mi ,…, mq , v1 ,…,vi ,…,vq, v),

aea: q – /enei eiiiiiaio ca’yciino? iaae? ia’?eoa S.

s1, s2 ,…,sq -noeoii?noue i?inoi?iaeo oi?i eiiiiiaio ca’yciino? iaae?
S;

m1, m2 ,…, mq – iao?e/i? oa?aeoa?enoeee, eio??, cie?aia,
aecia/athoue ?ici??e oi/eiaeo iiiaeei, ui iathoue i?inoi?ia? oi?ie
{s};

v1 ,…,vi ,…,vq – ia?aiao?e ?ici?uaiiy eiiiiiaio ca’yciino? iaae?
S;

v – ia?aiao?e ?ici?uaiiy ia’?eoa S.

Ioaea, aaiiao?e/ia ?ioi?iaoe?y g ?iaeoeo? S o iaaiiio iao?e/iiio
i?inoi?? H. O ?iaio? acaaae? ?icaeyaeathoueny a?eoiaoe/i? aaee?aeiae
i?inoi?e R2 ? R3, oi/a ie?ai? ?acoeueoaoe ?iciianthaeaeothoueny ? ia
i?inoi?e a?eueoi? aei??iino?.

Iniiaia caaea/a aeaii? ?iaioe i???ioiaaia ia iaaiee eean oi/eiaeo
iiiaeei, a naia eean j*-aaaaoieooiee?a (j*-aaaaoia?aiiee?a).

O ?icae?e? aiae?cothoueny ?nioth/? caniae aecia/aiiy iaiioeeiai
aaaaoieooiiai (aaaaoia?aiiiai) j*-ia’?eoa. O i?inoi?? R2 iao?e/i?
oa?aeoa?enoeee m1, m2,…,mq iiaeooue aooe cia?aaeai? eii?aeeiaoaie
aa?oei a?aeiia?aeieo aaaaoieooieo eiioo??a o aeani?e nenoai? eii?aeeiao,
ia?aiao?e ?ici?uaiiy iathoue aeaeyae v=(x,y,f).

sseui iieeanoe ia?aiao? f – eoo iiai?ioo aeanii? nenoaie eii?aeeiao
j*-ia’?eoa a?aeiinii ioey i?inoi?o – o?eniaaiei, aaaaoieooia iaeanoue
oaeiae iiaea aooe caaeaia aiae?oe/ii ca aeiiiiiaith aia?aoo no?oeoo?
e?i?eieo ia??aiinoae ((F(x),(,m), aea F(x) – oii?yaeeiaaiee iaa??
e?i?eieo ia??aiinoae, ye? caaeathoue e?i?ei? /anoeie iaae?
j*-aaaaoieooieea S, (= (((qg((m(m- iao?eoey a?aeiioaiue, m- e?euee?noue
ia??aiinoae.

O ?icae?e? iaaaaeaii aiae?c aia?aoo no?oeoo? e?i?eieo ia??aiinoae ye
iioe?aiiy iiiyooy nenoaie e?i?eieo ia??aiinoae ? caniao aiae?oe/iiai
iieno iaiioeei? eiiiaeoii? oi/eiai? iiiaeeie.

– e?euee?noue aa?oei a?ai? gr, N – e?euee?noue a?aiae. Aaeoi?
ia?aiao??a ?ici?uaiiy ia’?eoa S ia? aeaeyae: {v} = (X,Y, Z, f, y, q).

Iaoaiaoe/ia iiaeaeue Ak(Rt) (t=2,3) – iioei?caoe?eii? caaea/?
aaiiao?e/iiai i?iaeooaaiiy, ui ?icaeyaea?oueny o ?iaio?, ia? aeaeyae:

aecia/eoe aaeoi? u* ? a?aeiia?aeiee eiio ia?ac Su ( Rt, ui
?iaeoeo?oueny aaiiao?e/iith ?ioi?iaoe??th
g(u*)=P(g0(u0),g1(u1),…,gn(un)), i?e yeiio

, (1)

aea gi=(si, mi, vi) – aaiiao?e/ia ?ioi?iaoe?y, ui ?iaeoeo? iaiaaeai?
iaeiica’yci? j*-aaaaoieooieee (j*-aaaaoia?aiieee) Si, i=0,1,…n a Rt;

S0-iaeanoue ?ici?uaiiy;

g(u)-aaiiao?e/ia ?ioi?iaoe?y i?i oi/eiao iiiaeeio Su=B(S0, S1,…Sn),

A – iia?aoi?, ui ? eiiiiceoe??th oai?aoeei-iiiaeeiieo iia?aoe?e
aeaeyaeo

Si)

P- iia?aoi? aeaeyaeo:

Si)}, {m0, m1 …mn}, {v0 v1…vn}),

ui – aaeoi? ci?iieo gi(Gi, i=0,1,…n;

D – iaeanoue i?eionoeieo ?ica’yce?a.

Caoaaaeaiiy 1. Aeoiaey/e c ?aaeueieo a?aeiioaiue iaoa??aeueieo ia’?eo?a
i?e ?ici?uaii? a aeai?e iaeano?, ui iiaeaeththoueny o ?iaio?, iaeanoue D
aecia/a?oueny:

a) oiiaaie ?ici?uaiiy ia’?eo?a Sj a iaeano? S0

, j=1,2,…n, (2)

– a?aeiioaiiy aeeth/aiiy,

S^0=R2\int S0 – aeiiiaiaiiy oi/eiai? iiiaeeie S0 aei anueiai i?inoi?o,
a yeiio ?icaeyaea?oueny oi/eiaa iiiaeeia S0.

a) oiiaaie aca?iiiai iaia?aoeio ia’?eo?a, ui ?ici?uothoueny, aeaeyaeo

, i

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