optimatlashtirishning chiziqli programmalashtirish usuli

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1363791652_42640.doc www.arxiv.uz optimatlashtirishning chiziqli programmalashtirish usuli ðoâp qollarda maòsadli funktsiya quyidagi tipdagi oâz parametrlariga nisbatan chiziqli funktsiyalarda ifodalanadi [image: image1.wmf]( ) max min ... 2 1 1 â® + + = + = n n x c x c x c i agar bunday hollar uchun mavjud oblastli va chegaraviy funktsiyalar ham: [image: image2.wmf]a x a x a x n â³ â³ â³ ;... ; 2 1 [image: image3.wmf]1 2 12 1 11 ... b x a x a x a n n â£ + + + [image: image4.wmf]; ... 2 2 2 1 1 m n m m m b x a x a x a â£ + + + chiziqli funktsiyalar boâladigan boâlsa, bunday masalalar matematikada chiziqli programmalashtirish masalalari deb ataladi. maqsadli funktsiyadagi parametrlar soni ikkita yoki uchta boâlsa masalani eng oson grafik usulda echish mumkin. misol sifatida quyidagini koâraylik: [image: image5.wmf]2 1 5 _ 3 x x …

ksimallashtirish masalasida oâsish tomonga, minimallashtirish masalasida esa kamayish tomonga siljitib boriladi. bu siljitishlardagi maqsadli funktsiya chizigâining ruxsat etilgan oblast koâpburchagining eng soângida tark etgan uchi optimal echim koordinatasi boâladi. misolda jmax uchburchakni a nuqtada tark etadi, yaâni echim shu nuqtada boâladi [image: image13.wmf]( ) 0 , 4 2 2 = = ããã ããã ã x . agar parametrlar soni uchta boâlsa masalani fazodagi grafik tasvirlarda echishga toâgâri keladi va optimallashtirishning bu usulini qoâllanish qiyinchiliklarga olib keladi. amalda koâp parametrli masalalarni chiziqli programmalashtirish usulida echishda iteratsion-hisoblash usullari qoâllaniladi. bunday usullardan biri boâlgan simpleks usuli [3] da tavsiflangan. chiziqli programmalashtirish masalalarini echishning ham maxsus amaliy dasturlar toâplami mavjud. dasturlar toâplami yordamida bunday masalalarni eò²m da echish maqsadga muvofiqdir. optimallashtirishning variatsion hisoblash usuli yuqorida koârilgan masalalarning barchasida maqsadli va chegaraviy munosabatlar aniqlanishi kerak boâlgan parametrga nisbatan funktsiyalar sifatida berilgan edi. ts ni loyihalashda, baâzi hollarda maqsadli munosabatlar va chegaraviy munosabatlar funktsiyalar emas funktsionallar …

âriladi. eyler shartini qoâllanilishini yaxshi tushunib olish uchun avvalo quyidagi osonroq masalani koâraylik (16-rasm) [image: image17.png] 16-rasm. variatsion hisoblash usulini tushunishga doir a va v nuqalarni tutashtiruvchi u=u(x) shunday funktsiya aniqlansinki, shu funktsiya grafigi boâyicha harakatlangan a v chizigâi uzunligi minimal boâlsin. ðonkretroq boâlishi uchun a nuqta koordinatalari (x=0; u=0), v nuqta koordinatalari (x=1; u=1) boâlsin. rasmga asosan minimallashtirish kerak boâlgan integral quyidagicha ifodalanadi [image: image18.wmf]ã² ã² ã² + = + - = b a b a b a dx y dy dx ds i 2 1 2 2 ) ( 1 demak, f funktsiya quyidagicha boâladi. [image: image19.wmf]2 1 ) ( 1 y f + = bundan [image: image20.wmf]; 0 = â¶ â¶ y f [image: image21.wmf]; ) ( 1 2 1 1 1 y y y f + = â¶ â¶ [image: image22.wmf]ã· ã· ã¸ ã¶ ã§ ã§ ã¨ ã¦ + = 2 1 1 ) ( 1 …

gicha boâladi [image: image28.wmf]0 1 1 = â¶ + â¶ - â¶ â¶ - â¶ â¶ dy g dx d dy f dx d y g y f l l (28) misol tariqasida quyidagini koâraylik (17rasm) [image: image29.jpg] 17-rasm. variatsion hisoblash usuli misoliga doir a,v nuqtalarni tutashtiruvchi uzunligi minimal va grafigi ostidagi yuza s= [image: image30.wmf]p /r. ga teng boâlgan y=u(x) funktsiya aniqlansin. nuqtalar koordinatalari rasmda keltirilgan oldingi misolda aniqlanganidek [image: image31.wmf]min; ) ( 1 2 1 â® + = ã² dx y i b a [image: image32.wmf]ã² - = b a r ydx g p demak bu misol uchun, [image: image33.wmf]2 1 ) ( 1 y f + = va g=y eyler shartiga asosan [image: image34.wmf]0 0 ) ( 1 2 1 1 = + + y y dx d oxirgi differentsial tenglamani echsak [image: image35.wmf]) 1 ( 1 - = c l da [image: image36.wmf]2 x x y …

. texnologik tizim elementlarini matematik modellashtirish asoslari. oâquv qoâllanma. toshkent, 1996. 5. ðð¾ñðµð½ðºð¾ð² ð.ð. ðñð¸ð½ñð¸ð¿ñ ð¿ð¾ñññð¾ðµð½ð¸ñ ð¸ ññññðºññññ ð¡ððð . ð.: ðð°ñð¸ð½ð¾ñññðµð½ð¸ðµ, 1987. 6. ðð¾ñññðºð¾ ð.ð. ð¸ ð´ñ. ð¢ðµð¾ñðµñð¸ñðµñðºð¸ðµ ð¾ñð½ð¾ð²ñ ð¡ððð . ð£ñðµð±ð½ð¸ðº ð´ð»ñ ð²ñð·ð¾ð². ð.: ðð°ñð¸ð½ð¾ñññð¾ðµð½ð¸ðµ, 1987. _1231532640.unknown _1231535539.unknown _1255602528.unknown _1255603198.unknown _1255603470.unknown _1255603836.unknown _1255846855.unknown _1255604073.unknown _1255603551.unknown _1255603410.unknown _1255602877.unknown _1255603002.unknown _1231608374.unknown _1255526120.unknown _1255526818.unknown _1255602480.unknown _1231608993.unknown _1231535839.unknown _1231533940.unknown _1231534484.unknown _1231535507.unknown _1231534455.unknown _1231532808.unknown _1231533092.unknown _1231532694.unknown _1231531976.unknown _1231532218.unknown _1231532284.unknown _1231532172.unknown _1231531628.unknown _1231531868.unknown _1231531422.unknown

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1363791652_42640.doc www.arxiv.uz optimatlashtirishning chiziqli programmalashtirish usuli ðoâp qollarda maòsadli funktsiya quyidagi tipdagi oâz parametrlariga nisbatan chiziqli funktsiyalarda ifodalanadi [image: image1.wmf]( ) max min ... 2 1 1 â® + + = + = n n x c x c x c i agar bunday hollar uchun mavjud oblastli va chegaraviy funktsiyalar ham: [image: image2.wmf]a x a x a x n â³ â³ â³ ;... ; 2 1 [image: image3.wmf]1 2 12 1 11 ... b x a x a x a n n â£ + + + [image: image4.wmf]; ... 2 2 2 1 1 m n m m m b x a x a x a â£ + + + chiziqli funktsiyalar boâladigan boâlsa, bunday masalalar matematikada chiziqli programmalashtirish …

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