a3)595*! ! !

stu-s Sromebi – TRANSACTIONS OF GTU – ТРУДЫ ГТУ № 2 (484), 2012
romelic ukve geometriuli programirebis
meTodiT amoixsneba.
pirdapiri programisaTvis gvaqvs miznobrivi
funqcia
π e
g t = t t → , (8)
o () 3 4 min
iZulebiT SezRudvebs aqvs Semdegi saxe:
()
()
g1 g2 t
t
2 −1 −3 −1
= t1t3 + t2 t3
≤1⎫⎪⎬ −3 −1 2 −1
= t1 t4 + t2t4 ≤1⎪⎭ t > 0, t > 0, t > 0, t > 0.
1 2 3 4
g1 ( t ) da g2 ( t ) iZulebiTi SezRudvebi
Semdegi aRniSvnebiT miiReba:
t t t −
≥ + ;
2 3
3 1 2
t4 −3
t1 2
t2
≥ + .
amocanis oradi programa Camoyalibdeba
Semdegi saxiT:
δ1 δ2 δ3 δ4
δ5
(9)
⎛ 1 ⎞
ν ( δ)
= ⎜ ⎟
⎝δ1 ⎠
⎛ 1 ⎞
⎜ ⎟
⎝δ2 ⎠
⎛ 1 ⎞
⎜ ⎟
⎝δ3 ⎠
⎛ 1 ⎞
⎜ ⎟
⎝δ4 ⎠
⎛ 1 ⎞
⎜ ⎟
⎝δ5 ⎠
×
( ) ( ) δ2+ δ3 ( δ4+ δ5)
δ2 + δ3 ( δ4 + δ5)
→ max ;
δ ≥0; δ ≥0; δ ≥0; δ ≥0; δ ≥ 0.
(10)
1 2 3 4 5
normalizaciisa da orTogonalurobis
pirobebidan miviRebT gantolebaTa sistemas:
δ1
= 1, ⎫
2δ − 3δ = 0,
⎪
⎪⎪
2 4
− 3δ3 + 2δ5 = 0, ⎬
1− 2 − 3 = 0,
⎪
πδ δ δ
⎪
eδ1−δ4
− δ5
= 0. ⎪⎭
(11)
(11) sistemis amoxsna gvaZlevs δ i cvladebis
Semdeg sidideebs:
δ2= 95π − 65e= 2.393;
δ3= 6 5e − 4 5π = 0.749;
δ4= 65π − 45e= 1.595;
δ = 9 5e − 6 5π = 1.123.
5
δ i sidideebis (10)-Si SetaniT miviRebT:
0
() ( )
g t = ν δ = 35.5 .
amocanis amoxsnisas Tu romelime δ i nulis
tolia, meTodis moTxovnis Tanaxmad
δ δ miiReba 1-is toli.
t j parametrebis optimaluri sidideebi
gamoiTvleba tolobebidan:
2 −1
δ2
⎫
tt 1 3 = = 0.76
δ2 + δ ⎪
3 ⎪
−3 −1
δ3
⎪
t2 t3
= = 0.24⎪
δ2 + δ3
⎪
⎬⎪
−3 −1
δ 4
t1 t4
= = 0.60
δ4 + δ ⎪
5
⎪
2 −1
δ5
tt 2 4 = = 0.40
⎪
δ4 + δ ⎪
5 ⎭
(12)
(12) tolobebidan miviRebT t j parametrebis
optimalur sidideebs (galogariTmebiT):
12
t = 0.49; t = 2.35; t = 0.32; t = 13.80.
1 2 3 4
erTi wevrisagan Semdgari miznobrivi
funqcia (8), romelic oradi funqciis (10)
tolia, am SemTxvevaSi amoxsnis sisworis Se-
π e
samowmeblad gamoiyeneba: tt 3 4 = ν ( δ) × δ1
= 35.5 .
ν ( δ ) miznobrivi funqcia da t j parametrebi
SeiZleboda π da e sidideebis analizuri
damokidebulebebiT gamogvesaxa.
ganxiluli amocanebi naTlad aCvenebs geometriuli
programirebis meTodis efeqturobas
saTanadod formulirebuli optimaluri
daproeqtebis amocanebis amosaxsnelad.
ganxiluli meTodi gamoyenebul iqna tyibulis
qvanaxSiris Saxtebis ZiriTadi parametrebis
optimaluri sidideebis dasadgenad,
xarjebis minimumis kriteriumiT da qvanaxSiris
mopovebaze iZulebiTi SezRudviT
[3], agreTve naxSiris mompovebeli ubnebis
sawmendi sangrevis optimaluri parametrebis
dadgenisaTvis, samuSaoTa Sromatevadobis
minimumis kriteriumiT [4].
3. daskvna
naSromSi naCvenebia geometriuli programirebis
meTodis efeqturi, gamoyenebiTi
mxare teqnikuri sistemebisa da mowyobilobebis
optimizaciis praqtikuli sakiTxebis
gadawyetisas. efeqturoba gamoixateba eqstremaluri
amocanebis gadawyvetisas miznobrivi
funqciis da regulirebadi parametrebis
analizuri damokidebulebebis miRebaSi,
romlebic rogorc raodenobrivad, ise
xarisxobrivad migvaniSnebs, rogor gavaumjobesoT
proeqti optimaluri funqcionirebisaTvis.