dinamik dasturlash usuli. bellmanning funksional tenglamasi

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динамик программалаштириш усули 10-ma’ruza: dinamik dasturlash usuli. bellmanning funksional tenglamasi reja: 1. masalaning qo’yilishi. 2. masalaning yechilishi. 3. algoritm. 4. algoritmdan jadval yordamida foydalanish. tayanch ibora va so’zlar: dinamik dasturlash, jarayon, dinamik jarayonlar, matematik dasturlash, maqsad funksiyasi, resurs miqdori, resurs taqsimoti, xom ashyo, masalalar oilasi, bellman tenglamasi, bellman funksiyasi. dinamik dasturlash usuli dinamik dasturlash – ko’p bosqichli va dinamik jarayonlarni matematik dasturlash hamda optimal boshqarishning maxsus masalalarini yechish usulidir. quyida bu usulning matematik dasturlash masalalaridan bir tipiga qo’llanilishini ko’ramiz. 1. masalaning qo’yilishi. matematik dasturlashning quyidagi (1) masalasini qaraymiz. bu masalaning o’ziga xos xususiyati shundan iboratki, uning maqsad funksiyasi separabeldir, ya’ni bir o’zgaruvchili , funksiyalar yig’indisidan iborat. bir qator iqtisodiy masalalarni (1) masala ko’rinishida matematik modellashtirish mumkin. shunday masalalardan biri-resurslar taqsimoti haqidagi masaladir. u miqdordagi xom ashyo (resurs) va ta texnologik jarayonlar berilgan bo’lsin; agar xom ashyoning x miqdorini - texnologik jarayonda foydalansak, miqdordagi foyda olinishi ma’lum bo’lsa, maksimal umumiy foyda …

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bellman tenglamasidan va (asosiy bog’lanish tenglik shaklda bo’lgan holda boshlang’ich shartdan foydalanib ketma-ket funksiyalarini topamiz. oxirgi, uchinchi bosqichda (1) masalaning yechimini quramiz: ni funksiyaga maksimum beruvchi nuqta sifatida aniqlaymiz, ya’ni ni ham shunga o’xshash shartdan aniqlaymiz, bu yerda . shunday davom etib, nuqtalarni shartdan topamiz, bu yerda ni esa, shartdan topamiz (asosiy bog’lanish tenglik ko’rinishda bo’lganda esa, bo’ladi). (1) masala maqsad funksiyasining maksimal qiymati ga teng. eslatma. agar (1) masalada funksiyalar ham qavariq bo’lsa, funksiyalar ham qavariq bo’ladilar va demak qavariq funksiyalarning xossalariga ko’ra (4) tenglamaning o’ng tomonida maksimumga yo , yoki nuqtada erishiladi. 1-misol. resurslar taqsimoti haqidagi (2) masalada bo’lsin. shu masalani yechamiz. demak, quyidagi masala berilgan: unga o’xshash masalalar oilasi quyidagicha bo’ladi: bellman funksiyasi uchun bellman tenglamasini yozamiz: bu tenglama uchun boshlang’ich shart bo’ladi. bellman tenglamasidan ketma-ket va funksiyalarni topamiz: endi optimal taqsimotni aniqlaymiz. bu yerda maksimumga da erishiladi. demak, , bu yerda maksimumga da erishiladi. demak, . …

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soblaymiz hamda va ni eslab qolamiz; 8) agar bo’lsa, deb 6) punktga qaytamiz; aks holda navbatdagi punktga o’tamiz; 9) agar bo’lsa. , deb 6) bandga qaytamiz; aks holda navbatdagi bandga o’tamiz; 10) (1) masalani yechimi ni aniqlaymiz: (7) -(1) masala maqsad funksiyasining optimal qiymati bo’ladi. eslatma. agar (7) formulada biror uchun bo’lsa, bo’ladi. 4. algoritmdan jadval yordamida foydalanish qiymatlar bilan birga (6) ga maksimum beruvchi va (5) ga maksimum beruvchi sonlarni ham yozib qo’yamiz (agar (5) va (6) ga maksimum beruvchi nuqtalar bir nechta bo’lsa, ularning hammasi yoziladi). jadvalni to’ldirgandan so’ng (7) bo’yicha formula bo’yicha (1) masala yechimi ni osongina aniqlash mumkin. algoritmdan jadval yordamida foydalanish qo’lda bajariladigan hisoblashlar uchun tavsiya qilinadi. eslatma. asosiy bog’lanish tenglik ko’rinishda bo’lganda (ya’ni ) sonlarni jadvalga yozish shart emas. bu holda (1) masala yechimining koordinatasini formula bilan topamiz. 1-jadval 0 1 2 … … … … … … … … … … … …

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quyidagi masalalarni yeching: 1) 2) 3) 4) 5) 6) 7) 8) 2. dinamik dasturlash usuli bilan o’zgaruvchilar butun qiymatli bo’lgan quyidagi masalalarni yeching (jadvaldan foydalaning): 1) 2) 3) 4) 5) 6) 7) 8) mavzuni mustahkamlash uchun tavsiya etiladigan adabiyotlar 1. вагнер г. основы исследований операции. т. 1–3. м.: мир. 1972-73. 2. зайченко ю. б. исследование операций. киев. 1979. 3. таха х. введение в исследование операций. т. 1, 2. м.: мир. 1981. oleobject2.bin oleobject47.bin image48.wmf oleobject48.bin image49.wmf oleobject49.bin image50.wmf oleobject50.bin image51.wmf oleobject51.bin image52.wmf image3.wmf oleobject52.bin image53.wmf oleobject53.bin image54.wmf oleobject54.bin image55.wmf oleobject55.bin image56.wmf oleobject56.bin image57.wmf oleobject3.bin oleobject57.bin image58.wmf oleobject58.bin image59.wmf oleobject59.bin image60.wmf oleobject60.bin image61.wmf oleobject61.bin image62.wmf image4.wmf oleobject62.bin image63.wmf oleobject63.bin image64.wmf oleobject64.bin image65.wmf oleobject65.bin image66.wmf oleobject66.bin image67.wmf oleobject4.bin oleobject67.bin image68.wmf oleobject68.bin image69.wmf oleobject69.bin image70.wmf oleobject70.bin image71.wmf oleobject71.bin image72.wmf image5.wmf oleobject72.bin image73.wmf oleobject73.bin image74.wmf oleobject74.bin image75.wmf oleobject75.bin image76.wmf oleobject76.bin image77.wmf oleobject5.bin oleobject77.bin image78.wmf oleobject78.bin image79.wmf oleobject79.bin image80.wmf oleobject80.bin image81.wmf oleobject81.bin image82.wmf image6.wmf oleobject82.bin …

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oleobject97.bin image98.wmf oleobject98.bin image99.wmf oleobject99.bin image100.wmf oleobject100.bin image101.wmf oleobject101.bin image102.wmf image8.wmf oleobject102.bin image103.wmf oleobject103.bin image104.wmf oleobject104.bin image105.wmf oleobject105.bin image106.wmf oleobject106.bin image107.wmf oleobject8.bin oleobject107.bin image108.wmf oleobject108.bin image109.wmf oleobject109.bin image110.wmf oleobject110.bin image111.wmf oleobject111.bin image112.wmf image9.wmf oleobject112.bin image113.wmf oleobject113.bin image114.wmf oleobject114.bin image115.wmf oleobject115.bin image116.wmf oleobject116.bin image117.wmf oleobject9.bin oleobject117.bin image118.wmf oleobject118.bin image119.wmf oleobject119.bin image120.wmf oleobject120.bin image121.wmf oleobject121.bin image122.wmf image10.wmf oleobject122.bin image123.wmf oleobject123.bin image124.wmf oleobject124.bin image125.wmf oleobject125.bin image126.wmf oleobject126.bin image127.wmf oleobject10.bin oleobject127.bin image128.wmf oleobject128.bin image129.wmf oleobject129.bin image130.wmf oleobject130.bin image131.wmf oleobject131.bin image132.wmf image11.wmf oleobject132.bin image133.wmf oleobject133.bin image134.wmf oleobject134.bin image135.wmf oleobject135.bin image136.wmf oleobject136.bin image137.wmf oleobject11.bin oleobject137.bin image138.wmf oleobject138.bin image139.wmf oleobject139.bin image140.wmf oleobject140.bin image141.wmf oleobject141.bin image142.wmf image12.wmf oleobject142.bin image143.wmf oleobject143.bin image144.wmf oleobject144.bin image145.wmf oleobject145.bin image146.wmf oleobject146.bin image147.wmf oleobject12.bin oleobject147.bin image148.wmf oleobject148.bin image149.wmf oleobject149.bin image150.wmf oleobject150.bin image151.wmf oleobject151.bin image152.wmf image13.wmf oleobject152.bin image153.wmf oleobject153.bin image154.wmf oleobject154.bin image155.wmf oleobject155.bin image156.wmf oleobject156.bin image157.wmf oleobject13.bin oleobject157.bin image158.wmf oleobject15

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динамик программалаштириш усули 10-ma’ruza: dinamik dasturlash usuli. bellmanning funksional tenglamasi reja: 1. masalaning qo’yilishi. 2. masalaning yechilishi. 3. algoritm. 4. algoritmdan jadval yordamida foydalanish. tayanch ibora va so’zlar: dinamik dasturlash, jarayon, dinamik jarayonlar, matematik dasturlash, maqsad funksiyasi, resurs miqdori, resurs taqsimoti, xom ashyo, masalalar oilasi, bellman tenglamasi, bellman funksiyasi. dinamik dasturlash usuli dinamik dasturlash – ko’p bosqichli va dinamik jarayonlarni matematik dasturlash hamda optimal boshqarishning maxsus masalalarini yechish usulidir. quyida bu usulning matematik dasturlash masalalaridan bir tipiga qo’llanilishini ko’ramiz. 1. masalaning qo’yilishi. matematik dasturlashning quyidagi (1) masalasini qaraymiz. bu masalanin...

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