Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Методы оптимальных решений
.pdf
ɌȿɆȺ 4. Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ
4.1. Ɉɛɳɚɹɩɨɫɬɚɧɨɜɤɚɡɚɞɚɱɢɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ – ɷɬɨ ɦɚɬɟɦɚɬɢɱɟɫɤɢɣ ɦɟɬɨɞ
ɩɨɢɫɤɚ ɨɩɬɢɦɚɥɶɧɨɝɨ ɭɩɪɚɜɥɟɧɢɹ ɫɩɟɰɢɚɥɶɧɨ ɩɪɢɫɩɨɫɨɛɥɟɧɧɵɣ ɤ
ɦɧɨɝɨɲɚɝɨɜɵɦɩɪɨɰɟɫɫɚɦɊɚɫɫɦɨɬɪɢɦɩɪɢɦɟɪɬɚɤɨɝɨɩɪɨɰɟɫɫɚ
ɉɭɫɬɶɩɥɚɧɢɪɭɟɬɫɹɞɟɹɬɟɥɶɧɨɫɬɶ ɝɪɭɩɩɵɩɪɟɞɩɪɢɹɬɢɣɧɚ N ɥɟɬ
Ɂɞɟɫɶɲɚɝɨɦɹɜɥɹɟɬɫɹɨɞɢɧɝɨɞȼɧɚɱɚɥɟ-ɝɨ ɝɨɞɚ ɧɚ ɪɚɡɜɢɬɢɟ
ɩɪɟɞɩɪɢɹɬɢɣ ɜɵɞɟɥɹɸɬɫɹ ɫɪɟɞɫɬɜɚ ɤɨɬɨɪɵɟ ɞɨɥɠɧɵ ɛɵɬɶ ɤɚɤ-ɬɨ
ɪɚɫɩɪɟɞɟɥɟɧɵɦɟɠɞɭɷɬɢɦɢɩɪɟɞɩɪɢɹɬɢɹɦɢȼɩɪɨɰɟɫɫɟɢɯ
ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɜɵɞɟɥɟɧɧɵɟ ɫɪɟɞɫɬɜɚ ɱɚɫɬɢɱɧɨ ɪɚɫɯɨɞɭɸɬɫɹ
Ʉɚɠɞɨɟɩɪɟɞɩɪɢɹɬɢɟɡɚɝɨɞɩɪɢɧɨɫɢɬɧɟɤɨɬɨɪɵɣɞɨɯɨɞɡɚɜɢɫɹɳɢɣɨɬ
ɜɥɨɠɟɧɧɵɯ ɫɪɟɞɫɬɜ ȼ ɧɚɱɚɥɟ ɝɨɞɚ ɢɦɟɸɳɢɟɫɹ ɫɪɟɞɫɬɜɚ ɦɨɝɭɬ
ɩɟɪɟɪɚɫɩɪɟɞɟɥɹɬɶɫɹ ɦɟɠɞɭ ɩɪɟɞɩɪɢɹɬɢɹɦɢ ɤɚɠɞɨɦɭ ɢɡ ɧɢɯ
ɜɵɞɟɥɹɟɬɫɹɤɚɤɚɹ-ɬɨɞɨɥɹɫɪɟɞɫɬɜ
ɋɬɚɜɢɬɫɹ ɜɨɩɪɨɫ ɤɚɤ ɜ ɧɚɱɚɥɟ ɤɚɠɞɨɝɨ ɝɨɞɚ ɪɚɫɩɪɟɞɟɥɹɬɶ
ɢɦɟɸɳɢɟɫɹɫɪɟɞɫɬɜɚ ɦɟɠɞɭɩɪɟɞɩɪɢɹɬɢɹɦɢɱɬɨɛɵɫɭɦɦɚɪɧɵɣɞɨɯɨɞ
ɨɬɜɫɟɯɩɪɟɞɩɪɢɹɬɢɣɡɚN ɥɟɬɛɵɥɦɚɤɫɢɦɚɥɶɧɵɦ"
ɉɟɪɟɞɧɚɦɢɬɢɩɢɱɧɚɹɡɚɞɚɱɚɞɢɧɚɦɢɱɟɫɤɨɝɨɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
ɜɤɨɬɨɪɨɣɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹɭɩɪɚɜɥɹɟɦɵɣɩɪɨɰɟɫɫ– ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ
ɝɪɭɩɩɵɩɪɟɞɩɪɢɹɬɢɣɍɩɪɚɜɥɟɧɢɟɩɪɨɰɟɫɫɨɦɫɨɫɬɨɢɬɜɪɚɫɩɪɟɞɟɥɟɧɢɢ
ɢ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɢ ɫɪɟɞɫɬɜ ɍɩɪɚɜɥɹɸɳɢɦ ɜɨɡɞɟɣɫɬɜɢɟɦ ɍȼ
ɹɜɥɹɟɬɫɹ ɜɵɞɟɥɟɧɢɟ ɤɚɤɢɯ-ɬɨ ɫɪɟɞɫɬɜ ɤɚɠɞɨɦɭ ɢɡ ɩɪɟɞɩɪɢɹɬɢɣ ɜ
ɧɚɱɚɥɟɝɨɞɚ
ɍȼ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɞɨɥɠɧɨ ɜɵɛɢɪɚɬɶɫɹ ɫ ɭɱɟɬɨɦ ɜɫɟɯ ɟɝɨ
ɩɨɫɥɟɞɫɬɜɢɣ ɜ ɛɭɞɭɳɟɦ ɍȼ ɞɨɥɠɧɨ ɛɵɬɶ ɞɚɥɶɧɨɜɢɞɧɵɦ ɫ ɭɱɟɬɨɦ
ɩɟɪɫɩɟɤɬɢɜɵ ɇɟɬ ɫɦɵɫɥɚ ɜɵɛɢɪɚɬɶ ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɲɚɝɟ
ɧɚɢɥɭɱɲɟɟɍȼɟɫɥɢɜɞɚɥɶɧɟɣɲɟɦɷɬɨɩɨɦɟɲɚɟɬɩɨɥɭɱɢɬɶɧɚɢɥɭɱɲɢɟ
ɪɟɡɭɥɶɬɚɬɵ ɞɪɭɝɢɯ ɲɚɝɨɜ ɍȼ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɧɚɞɨ ɜɵɛɢɪɚɬɶ ³c
ɡɚɝɥɹɞɵɜɚɧɢɟɦɜɛɭɞɭɳɟɟ´ɢɧɚɱɟɜɨɡɦɨɠɧɵɫɟɪɶɟɡɧɵɟɨɲɢɛɤɢ
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ ɩɪɟɞɩɨɥɨɠɢɦ ɱɬɨ ɜ ɪɚɫɫɦɨɬɪɟɧɧɨɣ ɝɪɭɩɩɟ
ɩɪɟɞɩɪɢɹɬɢɣɨɞɧɢɡɚɧɹɬɵɜɵɩɭɫɤɨɦɩɪɟɞɦɟɬɨɜɩɨɬɪɟɛɥɟɧɢɹɚɞɪɭɝɢɟ
ɩɪɨɢɡɜɨɞɹɬɞɥɹɷɬɨɝɨɦɚɲɢɧɵɉɪɢɱɟɦɰɟɥɶɸɹɜɥɹɟɬɫɹɩɨɥɭɱɟɧɢɟɡɚN
ɥɟɬ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɨɛɴɟɦɚ ɜɵɩɭɫɤɚ ɩɪɟɞɦɟɬɨɜ ɩɨɬɪɟɛɥɟɧɢɹ ɉɭɫɬɶ
ɩɥɚɧɢɪɭɸɬɫɹ ɤɚɩɢɬɚɥɨɜɥɨɠɟɧɢɹ ɧɚ ɩɟɪɜɵɣ ɝɨɞ ɂɫɯɨɞɹ ɢɯ ɭɡɤɢɯ
ɢɧɬɟɪɟɫɨɜ ɞɚɧɧɨɝɨ ɲɚɝɚ ɝɨɞɚ ɦɵ ɞɨɥɠɧɵ ɛɵɥɢ ɛɵ ɜɫɟ ɫɪɟɞɫɬɜɚ
ɜɥɨɠɢɬɶɜ ɩɪɨɢɡɜɨɞɫɬɜɨɩɪɟɞɦɟɬɨɜ ɩɨɬɪɟɛɥɟɧɢɹɩɭɫɬɢɬɶɢɦɟɸɳɢɟɫɹ
ɦɚɲɢɧɵɧɚɩɨɥɧɭɸɦɨɳɧɨɫɬɶɢɞɨɛɢɬɶɫɹ ɤɤɨɧɰɭɝɨɞɚɦɚɤɫɢɦɚɥɶɧɨɝɨ
51
ɨɛɴɟɦɚɩɪɨɞɭɤɰɢɢɇɨɩɪɚɜɢɥɶɧɵɦ ɥɢɛɭɞɟɬ ɬɚɤɨɟɪɟɲɟɧɢɟ ɜɰɟɥɨɦ"
Ɉɱɟɜɢɞɧɨɧɟɬɂɦɟɹɜɜɢɞɭɛɭɞɭɳɟɟɧɟɨɛɯɨɞɢɦɨɜɵɞɟɥɢɬɶɤɚɤɭɸ-ɬɨ
ɞɨɥɸɫɪɟɞɫɬɜɢɧɚɩɪɨɢɡɜɨɞɫɬɜɨɦɚɲɢɧɉɪɢɷɬɨɦɨɛɴɟɦɩɪɨɞɭɤɰɢɢɡɚ
ɩɟɪɜɵɣ ɝɨɞ ɟɫɬɟɫɬɜɟɧɧɨ ɫɧɢɡɢɬɫɹ ɡɚɬɨ ɛɭɞɭɬ ɫɨɡɞɚɧɵ ɭɫɥɨɜɢɹ
ɩɨɡɜɨɥɹɸɳɢɟɭɜɟɥɢɱɢɜɚɬɶɟɟɩɪɨɢɡɜɨɞɫɬɜɨɜɩɨɫɥɟɞɭɸɳɢɟɝɨɞɵ
ȼ ɮɨɪɦɚɥɢɡɦɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɦɟɬɨɞɨɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹɛɭɞɭɬɢɫɩɨɥɶɡɨɜɚɬɶɫɹɫɥɟɞɭɸɳɢɟɨɛɨɡɧɚɱɟɧɢɹ
N – ɱɢɫɥɨɲɚɝɨɜ
21 nkkkk
ɫɢɫɬɟɦɵɧɚk-ɦɲɚɝɟ
– ɧɚɱɚɥɶɧɨɟɫɨɫɬɨɹɧɢɟɬɟcɨɫɬɨɹɧɢɟɧɚ-ɦɲɚɝɟ
x
0
– ɤɨɧɟɱɧɨɟɫɨɫɬɨɹɧɢɟɬɟFɨɫɬɨɹɧɢɟɧɚɩɨɫɥɟɞɧɟɦɲɚɝɟ
x
N
– ɨɛɥɚɫɬɶɞɨɩɭɫɬɢɦɵɯɫɨɫɬɨɹɧɢɣɧɚk-ɨɦɲɚɝɟ
X
k
21 mkkk
ɨɛɟɫɩɟɱɢɜɚɸɳɢɣɩɟɪɟɯɨɞɫɢɫɬɟɦɵɢɡɫɨɫɬɨɹɧɢɹx
– ɨɛɥɚɫɬɶɞɨɩɭɫɬɢɦɵɯɍȼɧɚk-ɨɦɲɚɝɟ
U
k
– ɜɟɥɢɱɢɧɚɜɵɢɝɪɵɲɚɩɨɥɭɱɟɧɧɨɝɨɜɪɟɡɭɥɶɬɚɬɟɪɟɚɥɢɡɚɰɢɢ
W
k
– ɜɟɤɬɨɪ ɨɩɢɫɵɜɚɸɳɢɣ ɫɨɫɬɨɹɧɢɟ
),....,,(
xxxx
– ɜɟɤɬɨɪ ɍȼ ɧɚ k-ɨɦ ɲɚɝɟ
),...,,(
uuuu
ɜɫɨɫɬɨɹɧɢɟxk.
k-1
k-ɝɨɲɚɝɚ
S – ɨɛɳɢɣɜɵɢɝɪɵɲɡɚN ɲɚɝɨɜ
*
1
ɭɩɪɚɜɥɟɧɢɹɢɥɢɈɍȼɡɚN ɲɚɝɨɜ
S
(
)–ɦɚɤɫɢɦɚɥɶɧɵɣ ɜɵɢɝɪɵɲ ɩɨɥɭɱɚɟɦɵɣ ɩɪɢ ɩɟɪɟɯɨɞɟ
x
k+1
k
ɢɡɥɸɛɨɝɨɫɨɫɬɨɹɧɢɹ
ɫɬɪɚɬɟɝɢɢɭɩɪɚɜɥɟɧɢɹɧɚɱɢɧɚɹɫk+1)-ɝɨɲɚɝɚ
S
(
)–ɦɚɤɫɢɦɚɥɶɧɵɣɜɵɢɝɪɵɲ ɩɨɥɭɱɚɟɦɵɣ ɡɚN ɲɚɝɨɜɩɪɢ
x
1
0
ɩɟɪɟɯɨɞɟ ɫɢɫɬɟɦɵ ɢɡ ɧɚɱɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ
ɪɟɚɥɢɡɚɰɢɢɨɩɬɢɦɚɥɶɧɨɣɫɬɪɚɬɟɝɢɢɭɩɪɚɜɥɟɧɢɹ
S
(
ɟɫɥɢ
x
1
0
– ɮɢɤɫɢɪɨɜɚɧɨ
x
0
**2*
– ɜɟɤɬɨɪ ɨɩɬɢɦɚɥɶɧɨɣ ɫɬɪɚɬɟɝɢɢ
),...,,(
uuuu
N
ɜɤɨɧɟɱɧɨɟɫɨɫɬɨɹɧɢɟ
x
k
ɩɪɢɨɩɬɢɦɚɥɶɧɨɣ
x
0
ɜ ɤɨɧɟɱɧɨɟ
x
0
*
ɈɱɟɜɢɞɧɨɱɬɨS=
u
ɩɪɢ
x
N
Ɇɟɬɨɞɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹɨɩɢɪɚɟɬɫɹ ɧɚɭɫɥɨɜɢɟ
ɨɬɫɭɬɫɬɜɢɹɩɨɫɥɟɞɟɣɫɬɜɢɹɢɭɫɥɨɜɢɟɚɞɞɢɬɢɜɧɨɫɬɢɰɟɥɟɜɨɣɮɭɧɤɰɢɢ
ɍɫɥɨɜɢɟ ɨɬɫɭɬɫɬɜɢɹ ɩɨɫɥɟɞɟɣɫɬɜɢɹɋɨɫɬɨɹɧɢɟ
ɩɟɪɟɲɥɚ ɫɢɫɬɟɦɚ ɡɚ ɨɞɢɧ k-ɣ ɲɚɝ ɡɚɜɢɫɢɬ ɨɬ ɫɨɫɬɨɹɧɢɹ
ɜ ɤɨɬɨɪɨɟ
x
k
x
ɢ
1k
52
ɜɵɛɪɚɧɧɨɝɨ ɍȼ
u
ɩɪɢɲɥɚɜɫɨɫɬɨɹɧɢɟ
kk
ɢ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɬɨɝɨ ɤɚɤɢɦ ɨɛɪɚɡɨɦ ɫɢɫɬɟɦɚ
k
ɬɨɟɫɬɶ
x
1k
uxfx
).,(
1 kk
ȺɧɚɥɨɝɢɱɧɨɜɟɥɢɱɢɧɚɜɵɢɝɪɵɲɚW
ɢɜɵɛɪɚɧɧɨɝɨɍȼ
ɬɨɟɫɬɶ
u
k
uxWW
1 kkkk
).,(
ɡɚɜɢɫɢɬɨɬɫɨɫɬɨɹɧɢɹ
k
x
1k
ɍɫɥɨɜɢɟɚɞɞɢɬɢɜɧɨɫɬɢɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɈɛɳɢɣɜɵɢɝɪɵɲɡɚN
ɲɚɝɨɜɜɵɱɢɫɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
N
1
k
Ɉɩɪɟɞɟɥɟɧɢɟ Ɉɩɬɢɦɚɥɶɧɨɣ ɫɬɪɚɬɟɝɢɟɣ ɭɩɪɚɜɥɟɧɢɹ
ɧɚɡɵɜɚɟɬɫɹ ɫɨɜɨɤɭɩɧɨɫɬɶ ɍȼ
*
1
uuuu
ɲɚɝɨɜ ɩɟɪɟɯɨɞɢɬɢɡ ɧɚɱɚɥɶɧɨɝɨ ɫɨɫɬɨɹɧɢɹ
uxWS
).,(
kkk
1
**2*
ɬɨ ɟɫɬɶ
,...,,
ɜ ɤɨɧɟɱɧɨɟ
x
0
uuu
N
x
N
1
**2*
ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɚɥɢɡɚɰɢɢɤɨɬɨɪɵɯ ɫɢɫɬɟɦɚ ɡɚ N
),...,,(
N
*
u
ɢ ɩɪɢ
ɷɬɨɦɨɛɳɢɣɜɵɢɝɪɵɲS ɩɪɢɧɢɦɚɟɬɧɚɢɛɨɥɶɲɟɟɡɧɚɱɟɧɢɟ
ɍɫɥɨɜɢɟɨɬɫɭɬɫɬɜɢɹɩɨɫɥɟɞɟɣɫɬɜɢɹɩɨɡɜɨɥɹɟɬɫɮɨɪɦɭɥɢɪɨɜɚɬɶ
ɩɪɢɧɰɢɩ ɨɩɬɢɦɚɥɶɧɨɫɬɢȻɟɥɥɦɚɧɚ
4ɉɪɢɧɰɢɩɨɩɬɢɦɚɥɶɧɨɫɬɢȻɟɥɥɦɚɧɚ
ɉɪɢɧɰɢɩ ɨɩɬɢɦɚɥɶɧɨɫɬɢ Ʉɚɤɨɜɨ ɛɵ ɧɢ ɛɵɥɨ ɞɨɩɭɫɬɢɦɨɟ
ɫɨɫɬɨɹɧɢɟ ɫɢɫɬɟɦɵ
ɜɵɛɪɚɬɶɞɨɩɭɫɬɢɦɨɟɍȼ
ɧɚi-ɦɲɚɝɟɩɥɸɫɨɩɬɢɦɚɥɶɧɵɣɜɵɢɝɪɵɲɧɚɜɫɟɯɩɨɫɥɟɞɭɸɳɢɯɲɚɝɚɯ
ɛɵɥɦɚɤɫɢɦɚɥɶɧɵɦ
ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɨɫɬɚɧɨɜɤɢ ɡɚɞɚɱɢ ɨɩɬɢɦɚɥɶɧɨɝɨ
ɭɩɪɚɜɥɟɧɢɹ ɩɪɨɞɨɥɠɢɦ ɪɚɫɫɦɨɬɪɟɧɢɟ ɡɚɞɚɱɢ ɭɩɪɚɜɥɟɧɢɹ
ɮɢɧɚɧɫɢɪɨɜɚɧɢɟɦ ɝɪɭɩɩɵ ɩɪɟɞɩɪɢɹɬɢɣ ɉɭɫɬɶ ɜ ɧɚɱɚɥɟ i-ɝɨ ɝɨɞɚ
ɝɪɭɩɩɟ ɩɪɟɞɩɪɢɹɬɢɣ
ɫɪɟɞɫɬɜɚ
iiXx
uuu
21 miii
ɩɟɪɟɞ ɨɱɟɪɟɞɧɵɦ i-ɦ ɲɚɝɨɦ ɧɚɞɨ
11
ɧɚɷɬɨɦɲɚɝɟɬɚɤɱɬɨɛɵɜɵɢɝɪɵɲW
Uu
ii
ɜɵɞɟɥɹɸɬɫɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
,...,,
21
.,...,,
m
ɫɨɜɨɤɭɩɧɨɫɬɶ ɷɬɢɯ ɡɧɚɱɟɧɢɣ ɦɨɠɧɨ
i
53
ɫɱɢɬɚɬɶ ɭɩɪɚɜɥɟɧɢɟɦ ɧɚi-ɦ ɲɚɝɟ ɬɨ ɟɫɬɶ
ɍɩɪɚɜɥɟɧɢɟ
ɜɫɟɯɲɚɝɨɜɵɯɭɩɪɚɜɥɟɧɢɣɬɨɟɫɬɶ
ɍɩɪɚɜɥɟɧɢɟ ɦɨɠɟɬ ɛɵɬɶ ɯɨɪɨɲɢɦ ɢɥɢ ɩɥɨɯɢɦ ɷɮɮɟɤɬɢɜɧɵɦ
ɢɥɢ ɧɟɷɮɮɟɤɬɢɜɧɵɦ ɗɮɮɟɤɬɢɜɧɨɫɬɶ ɭɩɪɚɜɥɟɧɢɹ
ɩɨɤɚɡɚɬɟɥɟɦ S ȼɨɡɧɢɤɚɟɬ ɜɨɩɪɨɫ ɤɚɤ ɜɵɛɪɚɬɶ ɲɚɝɨɜɵɟ ɭɩɪɚɜɥɟɧɢɹ
,...,,
21
ɉɨɫɬɚɜɥɟɧɧɚɹ ɡɚɞɚɱɚ ɹɜɥɹɟɬɫɹ ɡɚɞɚɱɟɣ ɨɩɬɢɦɚɥɶɧɨɝɨ
ɭɩɪɚɜɥɟɧɢɹ ɚ ɭɩɪɚɜɥɟɧɢɟ ɩɪɢ ɤɨɬɨɪɨɦ ɩɨɤɚɡɚɬɟɥɶ S ɞɨɫɬɢɝɚɟɬ
ɦɚɤɫɢɦɭɦɚ ɧɚɡɵɜɚɟɬɫɹ ɨɩɬɢɦɚɥɶɧɵɦ Ɉɩɬɢɦɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ
ɦɧɨɝɨɲɚɝɨɜɵɦ ɩɪɨɰɟɫɫɨɦ ɫɨɫɬɨɢɬ ɢɡ ɫɨɜɨɤɭɩɧɨɫɬɢ ɨɩɬɢɦɚɥɶɧɵɯ
ɲɚɝɨɜɵɯɭɩɪɚɜɥɟɧɢɣ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɩɟɪɟɞ ɧɚɦɢ ɫɬɨɢɬ ɡɚɞɚɱɚ ɨɩɪɟɞɟɥɢɬɶ
ɨɩɬɢɦɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ
ɨɩɬɢɦɚɥɶɧɨɟɭɩɪɚɜɥɟɧɢɟɜɫɟɦɩɪɨɰɟɫɫɨɦ
ɩɪɨɰɟɫɫɨɦ ɜ ɰɟɥɨɦ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣɫɨɜɨɤɭɩɧɨɫɬɶ
u
ɱɬɨɛɵɜɟɥɢɱɢɧɚS ɨɛɪɚɬɢɥɚɫɶɜɦɚɤɫɢɦɭɦ"
uuu
N
*
1
**2*
uuuu
),...,,(
N
u
.
),...,,(
uuuu
21 N
ɨɰɟɧɢɜɚɟɬɫɹ
u
*
(i 1 ɢ ɡɧɚɱɢɬ
u
i
*
.
),...,,(
uuuu
21 miiii
*
u
4.3. ɋɯɟɦɚɪɟɲɟɧɢɹɡɚɞɚɱɢɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ
.
Ɇɵɨɬɦɟɬɢɥɢɱɬɨɩɥɚɧɢɪɭɹɦɧɨɝɨɲɚɝɨɜɵɣɩɪɨɰɟɫɫ
ɧɟɨɛɯɨɞɢɦɨ ɜɵɛɢɪɚɬɶ ɍȼ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɫ ɭɱɟɬɨɦ ɟɝɨ ɛɭɞɭɳɢɯ
ɩɨɫɥɟɞɫɬɜɢɣɧɚɟɳɟɩɪɟɞɫɬɨɹɳɢɯɲɚɝɚɯɈɞɧɚɤɨɢɡɷɬɨɝɨɩɪɚɜɢɥɚɟɫɬɶ
ɢɫɤɥɸɱɟɧɢɟ ɋɪɟɞɢ ɜɫɟɯ ɲɚɝɨɜ ɫɭɳɟɫɬɜɭɟɬ ɨɞɢɧ ɤɨɬɨɪɵɣ ɦɨɠɟɬ
ɩɥɚɧɢɪɨɜɚɬɶɫɹ ɛɟɡ ɡɚɝɥɹɞɵɜɚɧɢɹ ɜ ɛɭɞɭɳɟɟ Ʉɚɤɨɣ ɷɬɨ ɲɚɝ"
Ɉɱɟɜɢɞɧɨ ɩɨɫɥɟɞɧɢɣ — ɩɨɫɥɟ ɧɟɝɨ ɞɪɭɝɢɯ ɲɚɝɨɜ ɧɟɬ ɗɬɨɬ ɲɚɝ
ɟɞɢɧɫɬɜɟɧɧɵɣɢɡɜɫɟɯ ɦɨɠɧɨɩɥɚɧɢɪɨɜɚɬɶɬɚɤɱɬɨɛɵɨɧ ɤɚɤɬɚɤɨɜɨɣ
ɩɪɢɧɟɫɧɚɢɛɨɥɶɲɭɸɜɵɝɨɞɭɋɩɥɚɧɢɪɨɜɚɜɨɩɬɢɦɚɥɶɧɨɷɬɨɬɩɨɫɥɟɞɧɢɣ
ɲɚɝɦɨɠɧɨɤɧɟɦɭɩɪɢɫɬɪɚɢɜɚɬɶɩɪɟɞɩɨɫɥɟɞɧɢɣɤɩɪɟɞɩɨɫɥɟɞɧɟɦɭ—
ɩɪɟɞɩɪɟɞɩɨɫɥɟɞɧɢɣɢɬɞ
ɉɨɷɬɨɦɭ ɩɪɨɰɟɫɫ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɧɚ -ɦ
ɷɬɚɩɟ ɪɚɡɜɨɪɚɱɢɜɚɟɬɫɹ ɨɬ ɤɨɧɰɚ ɤ ɧɚɱɚɥɭ ɬɨ ɟɫɬɶ ɪɚɧɶɲɟ ɜɫɟɯ
ɩɥɚɧɢɪɭɟɬɫɹɩɨɫɥɟɞɧɢɣ
N-ɣ ɲɚɝ Ⱥ ɤɚɤ ɟɝɨ ɫɩɥɚɧɢɪɨɜɚɬɶ ɟɫɥɢ ɦɵ ɧɟ ɡɧɚɟɦ ɱɟɦ
ɤɨɧɱɢɥɫɹ ɩɪɟɞɩɨɫɥɟɞɧɢɣ" Ɉɱɟɜɢɞɧɨ ɧɭɠɧɨ ɫɞɟɥɚɬɶ ɜɫɟ ɜɨɡɦɨɠɧɵɟ
54
ɩɪɟɞɩɨɥɨɠɟɧɢɹɨɬɨɦɱɟɦɤɨɧɱɢɥɫɹɩɪɟɞɩɨɫɥɟɞɧɢɣ
(N —
1)-ɣɲɚɝɢ
ɞɥɹ ɤɚɠɞɨɝɨ ɢɡ ɧɢɯ ɧɚɣɬɢ ɬɚɤɨɟ ɭɩɪɚɜɥɟɧɢɟ ɩɪɢ ɤɨɬɨɪɨɦ ɜɵɢɝɪɵɲ
ɞɨɯɨɞɧɚɩɨɫɥɟɞɧɟɦɲɚɝɟɛɵɥɛɵɦɚɤɫɢɦɚɥɟɧɊɟɲɢɜɷɬɭɡɚɞɚɱɭɦɵ
ɧɚɣɞɟɦ ɭɫɥɨɜɧɨ ɨɩɬɢɦɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ ɍɈɍ ɧɚN-ɦ ɲɚɝɟ ɬɟ
ɭɩɪɚɜɥɟɧɢɟɤɨɬɨɪɨɟ ɧɚɞɨɩɪɢɦɟɧɢɬɶɟɫɥɢN—1)-ɣɲɚɝ ɡɚɤɨɧɱɢɥɫɹ
ɨɩɪɟɞɟɥɟɧɧɵɦɨɛɪɚɡɨɦ
ɉɪɟɞɩɨɥɨɠɢɦɱɬɨɷɬɚɩɪɨɰɟɞɭɪɚɜɵɩɨɥɧɟɧɚɬɨɟɫɬɶɞɥɹ
ɤɚɠɞɨɝɨɢɫɯɨɞɚ
(N — 1)-ɝɨɲɚɝɚɦɵɡɧɚɟɦɍɈɍɧɚN-ɦɲɚɝɟɢɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ
ɟɦɭɭɫɥɨɜɧɨɨɩɬɢɦɚɥɶɧɵɣɜɵɢɝɪɵɲɍɈȼɌɟɩɟɪɶɦɵɦɨɠɟɦɨɩɬɢɦɢɡɢɪɨɜɚɬɶɭɩɪɚɜɥɟɧɢɟɧɚɩɪɟɞɩɨɫɥɟɞɧɟɦN —1)-ɦɲɚɝɟɋɞɟɥɚɟɦ ɜɫɟ
ɜɨɡɦɨɠɧɵɟ ɩɪɟɞɩɨɥɨɠɟɧɢɹ ɨ ɬɨɦɱɟɦ ɤɨɧɱɢɥɫɹ ɩɪɟɞɩɪɟɞɩɨɫɥɟɞɩɢɣ
ɬɨɟɫɬɶ(N — 2)-ɣɲɚɝɢɞɥɹɤɚɠɞɨɝɨɢɡɷɬɢɯɩɪɟɞɩɨɥɨɠɟɧɢɣɧɚɣɞɟɦ
ɬɚɤɨɟɭɩɪɚɜɥɟɧɢɟɧɚ(N —1)-ɦɲɚɝɟɱɬɨɛɵɜɵɢɝɪɵɲɡɚɩɨɫɥɟɞɧɢɟɞɜɚ
ɲɚɝɚ ɢɡ ɤɨɬɨɪɵɯ ɩɨɫɥɟɞɧɢɣ ɭɠɟ ɨɩɬɢɦɢɡɢɪɨɜɚɧ ɛɵɥ ɦɚɤɫɢɦɚɥɟɧ
Ⱦɚɥɟɟɨɩɬɢɦɢɡɢɪɭɟɬɫɹɭɩɪɚɜɥɟɧɢɟɧɚ(N — 2)-ɦɲɚɝɟɢɬɞ
Ɉɞɧɢɦ ɫɥɨɜɨɦ ɧɚ ɤɚɠɞɨɦ ɲɚɝɟ ɢɳɟɬɫɹ ɬɚɤɨɟ ɭɩɪɚɜɥɟɧɢɟ
ɤɨɬɨɪɨɟ ɨɛɟɫɩɟɱɢɜɚɟɬ ɨɩɬɢɦɚɥɶɧɨɟ ɩɪɨɞɨɥɠɟɧɢɟ ɩɪɨɰɟɫɫɚ
ɨɬɧɨɫɢɬɟɥɶɧɨɞɨɫɬɢɝɧɭɬɨɝɨɜɞɚɧɧɵɣɦɨɦɟɧɬɫɨɫɬɨɹɧɢɹɗɬɨɬɩɪɢɧɰɢɩ
ɜɵɛɨɪɚ ɭɩɪɚɜɥɟɧɢɹ ɧɚɡɵɜɚɟɬɫɹ ɩɪɢɧɰɢɩɨɦ ɨɩɬɢɦɚɥɶɧɨɫɬɢ ɋɚɦɨ
ɭɩɪɚɜɥɟɧɢɟ ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɨɩɬɢɦɚɥɶɧɨɟ ɩɪɨɞɨɥɠɟɧɢɟ ɩɪɨɰɟɫɫɚ
ɨɬɧɨɫɢɬɟɥɶɧɨɡɚɞɚɧɧɨɝɨɫɨɫɬɨɹɧɢɹɧɚɡɵɜɚɟɬɫɹɍɈɍɧɚɞɚɧɧɨɦɲɚ
ɝɟ
Ɍɟɩɟɪɶ ɩɪɟɞɩɨɥɨɠɢɦɱɬɨ ɍɈɍ ɧɚɤɚɠɞɨɦ ɲɚɝɟ ɧɚɦ ɢɡɜɟɫɬɧɨ
ɦɵɡɧɚɟɦɱɬɨɞɟɥɚɬɶɞɚɥɶɲɟɜɤɚɤɨɦɛɵɫɨɫɬɨɹɧɢɢɧɢɛɵɥɩɪɨɰɟɫɫɤ
ɧɚɱɚɥɭ ɤɚɠɞɨɝɨ ɲɚɝɚ Ɍɨɝɞɚ ɦɵ ɦɨɠɟɦ ɧɚɣɬɢ ɭɠɟ ɧɟ ɭɫɥɨɜɧɨɟ ɚ
ɞɟɣɫɬɜɢɬɟɥɶɧɨɨɩɬɢɦɚɥɶɧɨɟɭɩɪɚɜɥɟɧɢɟɧɚɤɚɠɞɨɦɲɚɝɟ
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ ɩɭɫɬɶ ɧɚɦ ɢɡɜɟɫɬɧɨ ɧɚɱɚɥɶɧɨɟ ɫɨɫɬɨɹɧɢɟ
ɩɪɨɰɟɫɫɚ Ɍɟɩɟɪɶ ɦɵ ɭɠɟ ɡɧɚɟɦ ɱɬɨ ɞɟɥɚɬɶ ɧɚ ɩɟɪɜɨɦ ɲɚɝɟ ɧɚɞɨ
ɩɪɢɦɟɧɢɬɶɍɈɍɧɚɣɞɟɧɧɨɟɞɥɹɩɟɪɜɨɝɨɲɚɝɚɢɧɚɱɚɥɶɧɨɝɨɫɨɫɬɨɹɧɢɹ
ȼɪɟɡɭɥɶɬɚɬɟɷɬɨɝɨɭɩɪɚɜɥɟɧɢɹ ɩɨɫɥɟɩɟɪɜɨɝɨɲɚɝɚɫɢɫɬɟɦɚɩɟɪɟɣɞɟɬɜ
ɞɪɭɝɨɟɫɨɫɬɨɹɧɢɟɧɨɞɥɹɷɬɨɝɨɫɨɫɬɨɹɧɢɹɦɵɡɧɚɟɦɍɈɍɢɝɞɌɚɤɢɦ
ɨɛɪɚɡɨɦɦɵɧɚɣɞɟɦɨɩɬɢɦɚɥɶɧɨɟɭɩɪɚɜɥɟɧɢɟɩɪɨɰɟɫɫɨɦɩɪɢɜɨɞɹɳɟɟ
ɤɦɚɤɫɢɦɚɥɶɧɨɜɨɡɦɨɠɧɨɦɭɜɵɢɝɪɵɲɭ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɜ ɩɪɨɰɟɫɫɟ ɨɩɬɢɦɢɡɚɰɢɢ ɭɩɪɚɜɥɟɧɢɹ ɦɟɬɨɞɨɦ
ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɦɧɨɝɨɲɚɝɨɜɵɣ ɩɪɨɰɟɫɫ
ɩɪɨɯɨɞɢɬɫɹɞɜɚɠɞɵ
ɉɟɪɜɵɣɪɚɡ— ɨɬɤɨɧɰɚɤɧɚɱɚɥɭɜɪɟɡɭɥɶɬɚɬɟɱɟɝɨɧɚɯɨɞɹɬɫɹ
ɍɈɍ ɧɚɤɚɠɞɨɦ ɲɚɝɟ ɢ ɨɩɬɢɦɚɥɶɧɵɣ ɜɵɢɝɪɵɲ ɬɨɠɟ ɭɫɥɨɜɧɵɣ ɧɚ
ɜɫɟɯɲɚɝɚɯɧɚɱɢɧɚɹɫɞɚɧɧɨɝɨɢɞɨɤɨɧɰɚɩɪɨɰɟɫɫɚ
ȼɬɨɪɨɣɪɚɡ— ɨɬɧɚɱɚɥɚɤɤɨɧɰɭɜɪɟɡɭɥɶɬɚɬɟɱɟɝɨɧɚɯɨɞɹɬɫɹ
ɨɩɬɢɦɚɥɶɧɵɟɭɩɪɚɜɥɟɧɢɹɧɚɜɫɟɯɲɚɝɚɯɩɪɨɰɟɫɫɚ
55
Ɇɨɠɧɨ ɫɤɚɡɚɬɶ ɱɬɨ ɩɪɨɰɟɞɭɪɚ ɩɨɫɬɪɨɟɧɢɹ ɨɩɬɢɦɚɥɶɧɨɝɨ
ɭɩɪɚɜɥɟɧɢɹɦɟɬɨɞɨɦɞɢɧɚɦɢɱɟɫɤɨɝɨɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹɪɚɫɩɚɞɚɟɬɫɹɧɚ
ɞɜɟ ɫɬɚɞɢɢ ɩɪɟɞɜɚɪɢɬɟɥɶɧɭɸɢ ɨɤɨɧɱɚɬɟɥɶɧɭɸ ɇɚ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ
ɫɬɚɞɢɢɞɥɹ ɤɚɠɞɨɝɨɲɚɝɚ ɨɩɪɟɞɟɥɹɟɬɫɹɍɈɍ ɡɚɜɢɫɹɳɟɟɨɬ ɫɨɫɬɨɹɧɢɹ
ɫɢɫɬɟɦɵ ɞɨɫɬɢɝɧɭɬɨɝɨ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɟɞɵɞɭɳɢɯ ɲɚɝɨɜ ɢ ɭɫɥɨɜɧɨ
ɨɩɬɢɦɚɥɶɧɵɣɜɵɢɝɪɵɲɧɚɜɫɟɯɨɫɬɚɜɲɢɯɫɹɲɚɝɚɯɧɚɱɢɧɚɹɫɞɚɧɧɨɝɨ
ɬɚɤɠɟɡɚɜɢɫɹɳɢɣɨɬɫɨɫɬɨɹɧɢɹɇɚɨɤɨɧɱɚɬɟɥɶɧɨɣɫɬɚɞɢɢɨɩɪɟɞɟɥɹɟɬɫɹ
ɛɟɡɭɫɥɨɜɧɨɟ ɨɩɬɢɦɚɥɶɧɨɟ ɭɩɪɚɜɥɟɧɢɟ ɞɥɹ ɤɚɠɞɨɝɨ ɲɚɝɚ
ɉɪɟɞɜɚɪɢɬɟɥɶɧɚɹ ɭɫɥɨɜɧɚɹ ɨɩɬɢɦɢɡɚɰɢɹ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɲɚɝɚɦ ɜ
ɨɛɪɚɬɧɨɦ ɩɨɪɹɞɤɟ ɨɬ ɩɨɫɥɟɞɧɟɝɨ ɲɚɝɚ ɤ ɩɟɪɜɨɦɭ ɨɤɨɧɱɚɬɟɥɶɧɚɹ
ɛɟɡɭɫɥɨɜɧɚɹ ɨɩɬɢɦɢɡɚɰɢɹ — ɬɚɤɠɟ ɩɨ ɲɚɝɚɦ ɧɨ ɜ ɟɫɬɟɫɬɜɟɧɧɨɦ
ɩɨɪɹɞɤɟɨɬɩɟɪɜɨɝɨɲɚɝɚɤɩɨɫɥɟɞɧɟɦɭɂɡɞɜɭɯɫɬɚɞɢɣɨɩɬɢɦɢɡɚɰɢɢ
ɧɟɫɪɚɜɧɟɧɧɨ ɛɨɥɟɟ ɜɚɠɧɨɣ ɢ ɬɪɭɞɨɟɦɤɨɣ ɹɜɥɹɟɬɫɹ ɩɟɪɜɚɹ ɉɨɫɥɟ
ɨɤɨɧɱɚɧɢɹ ɩɟɪɜɨɣ ɫɬɚɞɢɢ ɜɵɩɨɥɧɟɧɢɟ ɜɬɨɪɨɣ ɬɪɭɞɧɨɫɬɢ ɧɟ
ɩɪɟɞɫɬɚɜɥɹɟɬ ɨɫɬɚɟɬɫɹ ɬɨɥɶɤɨ ɩɪɨɱɟɫɬɶ ɪɟɤɨɦɟɧɞɚɰɢɢ ɭɠɟ
ɡɚɝɨɬɨɜɥɟɧɧɵɟɧɚɩɟɪɜɨɣɫɬɚɞɢɢ
4.4. ȼɵɛɨɪɫɨɫɬɚɜɚɨɛɨɪɭɞɨɜɚɧɢɹɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ
ɥɢɧɢɢ
Ɋɚɫɫɦɨɬɪɢɦ ɫɢɬɭɚɰɢɸ ɤɨɝɞɚ ɟɫɬɶ ɧɟɤɨɬɨɪɚɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɚɹ
ɥɢɧɢɹ ɬɨ ɟɫɬɶ ɰɟɩɨɱɤɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɢɡ -ɯ ɨɩɟɪɚɰɢɣ ɇɚ
ɤɚɠɞɭɸ ɨɩɟɪɚɰɢɸ ɦɨɠɧɨ ɧɚɡɧɚɱɢɬɶ ɨɛɨɪɭɞɨɜɚɧɢɟ ɬɨɥɶɤɨ ɤɚɤɨɝɨ-ɬɨ
ɨɞɧɨɝɨ ɜɢɞɚ ɚ ɨɛɨɪɭɞɨɜɚɧɢɹ ɫɩɨɫɨɛɧɨɝɨ ɪɚɛɨɬɚɬɶ ɧɚ ɞɚɧɧɨɣ
ɨɩɟɪɚɰɢɢ ɩɨ ɞɜɚ ɜɢɞɚ ɋɬɨɢɦɨɫɬɶ ɫɵɪɶɹ
ɫɜɹɡɚɧɧɵɟɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɟɞɢɧɢɰɵ ɨɛɨɪɭɞɨɜɚɧɢɹj-ɝɨɬɢɩɚ ɧɚ i-ɨɣ
ɨɩɟɪɚɰɢɢ ɫɨɫɬɚɜɥɹɸɬ
j-ɝɨɬɢɩɚɨɛɨɪɭɞɨɜɚɧɢɹɩɪɟɬɟɧɞɭɸɳɟɝɨɧɚi-ɸɨɩɟɪɚɰɢɸɩɨɜɵɯɨɞɭɢ
ɜɯɨɞɭɪɚɜɧɵ
ɂɫɯɨɞɧɵɟɞɚɧɧɵɟɞɥɹɩɪɢɦɟɪɚ
Ɉɛɨɪɭɞɨɜɚɧɢɟj121212
ɢ
x
ij
Ɉɩɟɪɚɰɢɹi123
x
ij
y
ij
ɉɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɞɥɹ
R
ij
.
y
ij
1084589
1284699
0
C
100
Ɋɚɫɯɨɞɵ
R
ij
20 18 6 8 10 12
56
Ⱦɥɹɬɨɝɨɱɬɨɛɵɪɟɲɢɬɶɞɚɧɧɭɸɡɚɞɚɱɭɦɟɬɨɞɨɦɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹɜɜɟɞɟɦɫɥɟɞɭɸɳɢɟɨɛɨɡɧɚɱɟɧɢɹ
= 3 – ɱɢɫɥɨɲɚɝɨɜ
N
- ɬɟɯɧɨɥɨɝɢɱɟɫɤɚɹɥɢɧɢɹ
x
i
= (0,0,0)
x
0
= (
x
N
– ɜɵɛɨɪɨɛɨɪɭɞɨɜɚɧɢɹɞɥɹi-ɨɣɨɩɟɪɚɰɢɢ
u
i
– ɨɛɥɚɫɬɶɞɨɩɭɫɬɢɦɵɯɍȼɧɚi-ɦɲɚɝɟ
U
i
W
i
ɪɟɡɭɥɶɬɚɬɟɪɟɚɥɢɡɚɰɢɢi-ɝɨɲɚɝɚ
S – ɮɭɧɤɰɢɹɨɛɳɟɝɨɜɵɢɝɪɵɲɚɬɟɦɢɧɢɦɚɥɶɧɚɹɫɟɛɟɫɬɨɢɦɨɫɬɶ
ɬɟ
,
Uu
ii
– ɨɰɟɧɤɚɦɢɧɢɦɚɥɶɧɨɣɫɟɛɟɫɬɨɢɦɨɫɬɢɩɨɥɭɱɟɧɧɚɹɜ
R
S
x
1
ɫɢɫɬɟɦɵɢɡɫɨɫɬɨɹɧɢɹ
*
*
1
ɨɛɟɫɩɟɱɢɜɚɸɳɢɣɩɟɪɟɯɨɞɫɢɫɬɟɦɵɢɡɫɨɫɬɨɹɧɢɹx
ɨɩɬɢɦɚɥɶɧɵɣɜɵɛɨɪɨɛɨɪɭɞɨɜɚɧɢɹɡɚN ɲɚɝɨɜ
ɦɢɧɢɦɚɥɶɧɚɹɫɟɛɟɫɬɨɢɦɨɫɬɶɩɨɥɭɱɚɟɦɵɣɩɪɢɩɟɪɟɯɨɞɟɢɡɥɸɛɨɝɨ
ɫɨɫɬɨɹɧɢɹ
ɭɩɪɚɜɥɟɧɢɹɧɚɱɢɧɚɹɫk+1)-ɝɨɲɚɝɚ
ɩɟɪɟɯɨɞɟɫɢɫɬɟɦɵɢɡɧɚɱɚɥɶɧɨɝɨɫɨɫɬɨɹɧɢɹ
ɪɟɚɥɢɡɚɰɢɢɨɩɬɢɦɚɥɶɧɨɣɫɬɪɚɬɟɝɢɢɭɩɪɚɜɥɟɧɢɹ
S
(
x
1
(
)–ɦɚɤɫɢɦɚɥɶɧɵɣɜɵɢɝɪɵɲɜɧɚɲɟɦɫɥɭɱɚɟ
S
x
i+1
i
ɜɤɨɧɟɱɧɨɟɫɨɫɬɨɹɧɢɟ
x
i
S
(
)–ɦɚɤɫɢɦɚɥɶɧɵɣɜɵɢɝɪɵɲɩɨɥɭɱɚɟɦɵɣɡɚN ɲɚɝɨɜɩɪɢ
x
1
0
ɟɫɥɢ
0
Ɂɚɩɢɲɟɦɜɟɤɬɨɪɚɞɨɩɭɫɬɢɦɵɯɡɧɚɱɟɧɢɣ
= 0.
x
0
)
,, uuu
321
u
2,1
1
u
2
u
3
y
j
1
x
j
1
- ɜɟɤɬɨɪ – ɮɭɧɤɰɢɹ ɨɩɢɫɵɜɚɸɳɚɹ ɩɟɪɟɯɨɞ
uux
iii
x
2
2,1
2,1
R
j
j
2
1
x
j
j
2
1
ɜɫɨɫɬɨɹɧɢɟ
1i
**
- ɜɟɤɬɨɪɍȼɧɚi-ɨɦɲɚɝɟ
),...,,(
uuuu
N
R
y
j
2
x
x
j
2
x
ɩɪɢɨɩɬɢɦɚɥɶɧɨɣɫɬɪɚɬɟɝɢɢ
x
0
y
j
3
j
3
ɩɨɞɞɟɣɫɬɜɢɟɦɍȼ
i
x
j
3
C
0
x
ɜɤɨɧɟɱɧɨɟ
0
u
j
3
ɜɫɨɫɬɨɹɧɢɟxiɬɟ
i-1
*
ɈɱɟɜɢɞɧɨɱɬɨS=
.
ɩɪɢ
x
N
57
ux
11
Ɂɚɩɢɲɟɦɜɟɤɬɨɪɚɞɨɩɭɫɬɢɦɵɯɭɩɪɚɜɥɹɸɳɢɯɜɨɡɞɟɣɫɬɜɢɣ
uu
11
Ɂɚɩɢɲɟɦɜɟɤɬɨɪ– ɮɭɧɤɰɢɸɨɩɢɫɵɜɚɸɳɭɸɩɟɪɟɯɨɞɫɢɫɬɟɦɵɢɡ
ɫɨɫɬɨɹɧɢɹ
ɭɠɟɧɟɛɭɞɟɬɚɬɚɤɠɟɬɨɱɬɨɦɵɧɚɨɛɪɚɬɧɨɦɩɪɨɯɨɞɟɜɦɟɫɬɨɮɭɧɤɰɢɢ
ɜɨɡɶɦɟɦɫɬɨɢɦɨɫɬɶɫɵɪɶɹ
S
4
ɜ ɫɨɫɬɨɹɧɢɟ
x
1i
Ɂɚɩɢɲɟɦɨɫɧɨɜɧɨɟɮɭɧɤɰɢɨɧɚɥɶɧɨɟɭɪɚɜɧɟɧɢɟ
Ɉɛɪɚɬɧɵɣɩɪɨɯɨɞ
Ⱦɥɹi=3:
ɍɱɢɬɵɜɚɹ ɬɨ ɱɬɨ ɷɬɨɬ ɲɚɝ ɩɨɫɥɟɞɧɢɣ ɢ ɫɥɟɞɭɸɳɟɣ ɨɩɟɪɚɰɢɢ
;
)0,0,(
;
)0,0,(
xS
ii
xS
23
uu
uuxx
1101
min
Uu
i
min
Uu
i
uux
22
x
i
i
;
)0,,(
212
;
)0,,0(
ɩɨɞɞɟɣɫɬɜɢɟɦɍȼ
i
)0,0,(
;
uuuuxx
321323
0
y
R
C
x
R
x
ij
ij
3
3
100
ij
x
ij
y
3
j
j
x
3
j
j
:
.
),,(
uuux
3213
uu
),0,0(
.
33
.
),,(
uxfS
111
)()(
uxS
324
;
)0,,(
uuuxx
21212
)),(()(
iiii
ɩɪɢ
ɩɪɢ
ɬɟ
u
)1,0,0(3
u
*
u
3
xS
:
=
=
)2,0,0(
10
)2,0,0(3
12
,
23
9
8
8
xS
23
9
9
9
*
S
3
58
min)( C
R
x
7,113100
min)( C
3,101100
.
3,101
y
31
x
31
;
R
32
x
32
;
31
31
=
0
y
x
32
32
=
0
Ⱦɥɹi=2:
xS
12
y
R
x
2
2
2
j
j
x
2
j
j
)(min)(
uxS
213
ɩɪɢ
ɩɪɢ
ɬɟ
Ⱦɥɹi=1:
ɩɪɢ
ɩɪɢ
u
2
u
u
u
*
u
2
)1,1,0(
)2,2,0(2
xS
:
4
6
=
4
4
:
)1,2,0(2
6
8
5
5
:
)2,1,0(2
4
6
=
4
4
xS
12
8
=
5
2,1,0
, 8,102
*
S .
3
xS
01
R
7,113
7,113
3,101
x
115,2
138,04
102,8;
R
22
x
22
3,101
12
xS
12
xS
12
6
21
21
R
22
x
22
R
21
x
21
123,1;
y
21
x
21
y
22
x
22
y
21
x
21
y
22
x
22
uxS
)(min)(
uxS
=
213
=
)(min)(
uxS
213
=
)(min)(
uxS
213
=
)(min)(
213
5
y
R
x
1
1
1
j
j
x
1
j
j
;
)(min)(
uxS
102
59
ɩɪɢ
u
u
ɩɪɢ
ɩɪɢ
u
ɩɪɢ
u
u ,
ɩɪɢ
)1,1,1(1
xS
01
12
20
=
10
10
2,115
R
11
x
11
140,2;
y
11
x
11
xS
)2,1,1(1
01
12
20
=
=
)1,2,1(1
=
10
18
20
10
10
)1,1,2(1
xS
01
8
18
=
)2,1,2(1
8
8
,
xS
01
8
8
8
xS
01
12
10
8,102
R
11
x
11
R
11
x
11
125,3;
R
12
x
12
R
12
x
12
05,1058,102
44,1387,113
y
11
x
11
y
12
x
12
;
45,1172,115
y
12
x
12
;
y
11
x
11
;
uxS
=
)(min)(
uxS
102
)(min)(
uxS
=
102
=
)(min)(
uxS
102
=
)(min)(
uxS
102
=
)(min)(
102
60
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]