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2 Модели и методы для выбора структуры ВС2.1 РЕШЕНИЕ ЗАДАЧИ «Расчет кратчайшей сети заданной конфигурации»
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РЕШЕНИЕ ЗАДАЧИ «Расчет кратчайшей сети заданной конфигурации» Л.И.
Абросимов, (г. Москва, Московский
энергетический институт (Технический университет), Россия
) Формулировка
задачи
Задана конфигурация сети
S- последовательная
двунаправленная шина, дуги которой соединяют узлы ai
1ó2ó3ó4ó5ó6ó7ó8ó9 Конфигурацию S можно записать в виде
матрицы S. Матрица S:
Рисунок
1 Известно также распределение
точек ba в
пространстве: Расстояния между точками
также записываются в виде матрицы M. Требуется распределить узлы
по точкам ba , размещённым в
пространстве на расстоянии
mab друг от друга таким образом, чтобы
суммарная взвешенная длина рассматриваемой сети была
минимальной. Матрица M:
Рисунок
2 Иначе говоря, требуется
«раскидать шары по лункам».
a1
ai …
a9
b1
ba
…
b9
Рисунок
3 Распределение записывается в
виде списка y таким образом:
y={ai}. В списке перечисляются номера
Решение задачи. Алгоритм
решения. 1. Исходные данные:
N=9, || Sij
||, i,j=1,…,N; || mab || , a,b=1,…,N; Начальное значение целевой
функции Q0=∞; {yi}*= {0}
(i=1,…,N), ω = № варианта mod 9 = 1 mod 9 = 1 2. Формирование для варианта
ω исходного списка {yi}ω по соотношению (1)
для
(i + ω –1) для 1
≤ i ≤ (N –ω +1);
yi ω =
(1)
(i + ω – N –1) для i
> (N –ω +1). 3. Расчёт цен Сi
0ω для i=1,…, N по соотношению (2) и
формирование списка {Сi
0ω}
4. Расчёт цен
Сij
Пω для i,j=1,…,N по соотношению (3) и
формирование матрицы
||Сij
Пω||
5.
Расчёт оценки Qijω по соотношению
(4).
(4) 6. Расчёт минимальной
оценки min Q и фиксирование номеров
i*,j*, которые соответствуют min Q. 7. Проверка, если
min Q <0, то перейти к п. 8,
иначе – к п. 9. 8. Корректировка исходного
списка {yi}ω за счёт перестановок
p:=yi* , v:=yj*
yi*:=v , yj*:=p и переход к
п.3 9. Расчёт Qω
по
соотношению (5)
N=9
N=9
Qω = ∑ ∑ Sij · myi
yj
(5)
i=1
j=1 10. Если Qω < Q0, то перейти к п.11, если
Qω≥Q0, то перейти к
п.12 11. Корректировка
оптимального значения целевой функции Q0 := Qω и списка оптимального решения {yi}*={yi}ω 12. Корректировка номера
исходного варианта ω:=ω+1 13. Если номер исходного
варианта ω≤N, то перейти к п.2, иначе –
к п.14 14. Вывод результата расчёта
оптимального значения целевой функции Q0 и списка оптимального решения {yi}*. Пример пошагового решения задачи по заданным выше исходным данным, соответствующим П1 Для иллюстрации представим расположение в
пространстве гнезд соответствующее матрице М следующим
образом:
b6
b3
b8
Рисунок 4
П.2
алгоритма
Для первого варианта ω =
1 y
= { 1, 2, 3, 4, 5, 6, 7, 8, 9}
Рисунок
5 П.3
алгоритма
Итерация 1:
С1
01
=S[1,1]*m[1,1] + S[1,1]*m[1,1] + S[1,2]*m[1,2] + S[2,1]*m[2,1] +
S[1,3]*m[1,3] + S[3,1]*m[3,1] + S[1,4]*m[1,4] + S[4,1]*m[4,1] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] + S[1,6]*m[1,6] + S[6,1]*m[6,1] + S[1,7]*m[1,7] + S[7,1]*m[7,1] +
S[1,8]*m[1,8] + S[8,1]*m[8,1] + S[1,9]*m[1,9] +
S[9,1]*m[9,1] С2
01 =S[2,1]*m[2,1] +
S[1,2]*m[1,2] + S[2,2]*m[2,2] + S[2,2]*m[2,2] + S[2,3]*m[2,3] +
S[3,2]*m[3,2] + S[2,4]*m[4,2] + S[4,2]*m[4,2] + S[2,5]*m[2,5] +
S[5,2]*m[5,2] + S[2,6]*m[2,6] + S[6,2]*m[6,2] + S[2,7]*m[2,7] + S[7,2]*m[7,2] +
S[2,8]*m[2,8] + S[8,2]*m[8,2] + S[2,9]*m[2,9]+
S[9,2]*m[9,2] С3
01=S[3,1]*m[3,1]
+ S[1,3]*m[1,3] + S[3,2]*m[3,2] + S[2,3]*m[2,3] + S[3,3]*m[3,3] +
S[3,3]*m[3,3] + S[3,4]*m[3,4] + S[4,3]*m[4,3] + S[3,5]*m[3,5] +
S[5,3]*m[5,3] + S[3,6]*m[3,6] + S[6,3]*m[6,3] + S[3,7]*m[3,7] + S[7,3]*m[7,3] +
S[3,8]*m[3,8] + S[8,3]*m[8,3] + S[3,9]*m[3,9] +
S[9,3]*m[9,3] С4
01
=S[4,1]*m[4,1] + S[1,4]*m[1,4] + S[4,2]*m[4,2] + S[2,4]*m[2,4] +
S[4,3]*m[4,3] + S[3,4]*m[3,4] + S[4,4]*m[1,1] + S[4,4]*m[1,1] +
S[4,5]*m[4,5] + S[5,4]*m[5,4] + S[4,6]*m[4,6] + S[6,4]*m[6,4] +
S[4,7]*m[4,7] + S[7,4]*m[7,4] + S[4,8]*m[4,8] + S[8,4]*m[8,4] + S[4,9]*m[4,9]+
S[9,4]*m[9,4] С5
01
=S[5,1]*m[5,1] + S[1,5]*m[1,5] + S[5,2]*m[5,2] + S[2,5]*m[2,5] + S[5,3]*m[5,3] +
S[3,5]*m[3,5] + S[5,4]*m[5,4] + S[4,5]*m[4,5] + S[5,5]*m[5,5] +
S[5,5]*m[5,5] + S[5,6]*m[5,6] + S[6,5]*m[6,5] + S[5,7]*m[5,7] +
S[7,5]*m[7,5] + S[5,8]*m[5,8] + S[8,5]*m[8,5] + S[5,9]*m[5,9] +
S[9,5]*m[9,5] С6
01
=S[6,1]*m[6,1] + S[1,6]*m[1,6] + S[6,2]*m[6,2] + S[2,6]*m[2,6] + S[6,3]*m[6,3] +
S[3,6]*m[3,6] + S[6,4]*m[6,4] + S[4,6]*m[4,6] + S[6,5]*m[6,5] +
S[5,6]*m[5,6] + S[6,6]*m[6,6] + S[6,6]*m[6,6] + S[6,7]*m[6,7] +
S[7,6]*m[7,6] + S[6,8]*m[6,8] + S[8,6]*m[8,6] + S[6,9]*m[6,9] +
S[9,6]*m[9,6] С7
01
=S[7,1]*m[7,1] + S[1,7]*m[1,7] + S[7,2]*m[7,2] + S[2,7]*m[2,7] + S[7,3]*m[7,3] +
S[3,7]*m[3,7] + S[7,4]*m[7,4] + S[4,7]*m[4,7] + S[7,5]*m[7,5] + S[5,7]*m[5,7] +
S[7,6]*m[7,6] + S[6,7]*m[6,7] + S[7,7]*m[7,7] + S[7,7]*m[7,7] +
S[7,8]*m[7,8] + S[8,7]*m[8,7] + S[7,9]*m[7,9]+
S[9,7]*m[9,7] С8
01
=S[8,1]*m[8,1] + S[1,8]*m[1,8] + S[8,2]*m[8,2] + S[2,8]*m[2,8] + S[8,3]*m[8,3] +
S[3,8]*m[3,8] + S[8,4]*m[8,4] + S[4,8]*m[4,8] + S[8,5]*m[8,5] + S[5,8]*m[5,8] +
S[8,6]*m[8,6] + S[6,8]*m[6,8] + S[8,7]*m[8,7] + S[7,8]*m[7,8] +
S[8,8]*m[8,8] + S[8,8]*m[8,8] + S[8,9]*m[8,9] +
S[9,8]*m[9,8] С9
01
=S[9,1]*m[9,1] + S[1,9]*m[1,9] + S[9,2]*m[9,2] + S[2,9]*m[2,9] + S[9,3]*m[9,3] +
S[3,9]*m[3,9] + S[9,4]*m[9,4] + S[4,9]*m[4,9] + S[9,5]*m[9,5] + S[5,9]*m[5,9] +
S[9,6]*m[9,6] + S[6,9]*m[6,9] + S[9,7]*m[9,7] + S[7,9]*m[7,9] +
S[9,8]*m[9,8] + S[8,9]*m[8,9] + S[9,9]*m[9,9] +
S[9,9]*m[9,9] С
01
={30, 60, 80, 100, 130, 104, 60 , 116, 80 } П.
4
алгоритма С11
Пω
=
S[1,1]*m[1,1] + S[1,1]*m[1,1] + S[1,2]*m[1,2] + S[2,1]*m[2,1] +
S[1,3]*m[1,3] + S[3,1]*m[3,1] + S[1,4]*m[1,4] + S[4,1]*m[4,1] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] + S[1,6]*m[1,6] + S[6,1]*m[6,1] + S[1,7]*m[1,7] + S[7,1]*m[7,1] +
S[1,8]*m[1,8] + S[8,1]*m[8,1] + S[1,9]*m[1,9] + S[9,1]*m[9,1] + S[1,1]*m[1,1] +
S[1,1]*m[1,1] С12
Пω
=
S[1,1]*m[2,1] + S[1,1]*m[1,2] + S[1,2]*m[2,2] + S[2,1]*m[2,2] + S[1,3]*m[2,3] +
S[3,1]*m[3,2] + S[1,4]*m[2,4] + S[4,1]*m[4,2] + S[1,5]*m[2,5] + S[5,1]*m[5,2] +
S[1,6]*m[2,6] + S[6,1]*m[6,2] + S[1,7]*m[2,7] + S[7,1]*m[7,2] + S[1,8]*m[2,8] +
S[8,1]*m[8,2] + S[1,9]*m[2,9] + S[9,1]*m[9,2] + S[1,2]*m[1,2] +
S[2,1]*m[2,1] C13 Пω
= S[1,1]*m[3,1] + S[1,1]*m[1,3] + S[1,2]*m[3,2] + S[2,1]*m[2,3] +
S[1,3]*m[3,3] + S[3,1]*m[3,3] + S[1,4]*m[3,4] + S[4,1]*m[4,3] + S[1,5]*m[3,5] +
S[5,1]*m[5,3] + S[1,6]*m[3,6] + S[6,1]*m[6,3] + S[1,7]*m[3,7] + S[7,1]*m[7,3] +
S[1,8]*m[3,8] + S[8,1]*m[8,3] + S[1,9]*m[3,9] + S[9,1]*m[9,3] + S[1,3]*m[1,3] +
S[3,1]*m[3,1] С14
Пω
=
S[1,1]*m[4,1] + S[1,1]*m[1,4] + S[1,2]*m[4,2] + S[2,1]*m[2,4] +
S[1,3]*m[4,3] + S[3,1]*m[3,4] + S[1,4]*m[4,4] + S[4,1]*m[4,4] + S[1,5]*m[4,5] +
S[5,1]*m[5,4] + S[1,6]*m[4,6] + S[6,1]*m[6,4] + S[1,7]*m[4,7] + S[7,1]*m[7,4] +
S[1,8]*m[4,8] + S[8,1]*m[8,4] + S[1,9]*m[4,9] + S[9,1]*m[9,4] + S[1,4]*m[1,4] +
S[4,1]*m[4,1] С15
Пω =
S[1,1]*m[5,1] + S[1,1]*m[1,5] + S[1,2]*m[5,2] + S[2,1]*m[2,5] +
S[1,3]*m[5,3] + S[3,1]*m[3,5] + S[1,4]*m[5,4] + S[4,1]*m[4,5] + S[1,5]*m[5,5] +
S[5,1]*m[5,5] + S[1,6]*m[5,6] + S[6,1]*m[6,5] + S[1,7]*m[5,7] + S[7,1]*m[7,5] +
S[1,8]*m[5,8] + S[8,1]*m[8,5] + S[1,9]*m[5,9] + S[9,1]*m[9,5] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] С16
Пω =
S[1,1]*m[6,1] + S[1,1]*m[1,6] + S[1,2]*m[6,2] + S[2,1]*m[2,6] +
S[1,3]*m[6,3] + S[3,1]*m[3,6] + S[1,4]*m[6,4] + S[4,1]*m[4,6] + S[1,5]*m[6,5] +
S[5,1]*m[5,6] + S[1,6]*m[6,6] + S[6,1]*m[6,6] + S[1,7]*m[6,7] + S[7,1]*m[7,6] +
S[1,8]*m[6,8] + S[8,1]*m[8,6] + S[1,9]*m[6,9] + S[9,1]*m[9,6] + S[1,6]*m[1,6] +
S[6,1]*m[6,1] С17
Пω =
S[1,1]*m[7,1] + S[1,1]*m[1,7] + S[1,2]*m[7,2] + S[2,1]*m[2,7] +
S[1,3]*m[7,3] + S[3,1]*m[3,7] + S[1,4]*m[7,4] + S[4,1]*m[4,7] + S[1,5]*m[7,5] +
S[5,1]*m[5,7] + S[1,6]*m[7,6] + S[6,1]*m[6,7] + S[1,7]*m[7,7] + S[7,1]*m[7,7] +
S[1,8]*m[7,8] + S[8,1]*m[8,7] + S[1,9]*m[7,9] + S[9,1]*m[9,7] + S[1,7]*m[1,7] +
S[7,1]*m[7,1] С18
Пω =
S[1,1]*m[8,1] + S[1,1]*m[1,8] + S[1,2]*m[8,2] + S[2,1]*m[2,8] +
S[1,3]*m[8,3] + S[3,1]*m[3,8] + S[1,4]*m[8,4] + S[4,1]*m[4,8] + S[1,5]*m[8,5] +
S[5,1]*m[5,8] + S[1,6]*m[8,6] + S[6,1]*m[6,8] + S[1,7]*m[8,7] + S[7,1]*m[7,8] +
S[1,8]*m[8,8] + S[8,1]*m[8,8] + S[1,9]*m[8,9] + S[9,1]*m[9,8] + S[1,8]*m[1,8] +
S[8,1]*m[8,1] С19
Пω
[1,9]= S[1,1]*m[9,1] + S[1,1]*m[1,9] + S[1,2]*m[9,2] +
S[2,1]*m[2,9] + S[1,3]*m[9,3] + S[3,1]*m[3,9] + S[1,4]*m[9,4] +
S[4,1]*m[4,9] + S[1,5]*m[9,5] + S[5,1]*m[5,9] + S[1,6]*m[9,6] + S[6,1]*m[6,9] +
S[1,7]*m[9,7] + S[7,1]*m[7,9] + S[1,8]*m[9,8] + S[8,1]*m[8,9] + S[1,9]*m[9,9] +
S[9,1]*m[9,9] + S[1,9]*m[1,9] + S[9,1]*m[9,1] С21
Пω =
S[2,1]*m[1,1] + S[1,2]*m[1,1] + S[2,2]*m[1,2] + S[2,2]*m[2,1] +
S[2,3]*m[1,3] + S[3,2]*m[3,1] + S[2,4]*m[1,4] + S[4,2]*m[4,1] +
S[2,5]*m[1,5] + S[5,2]*m[5,1] + S[2,6]*m[1,6] + S[6,2]*m[6,1] + S[2,7]*m[1,7] +
S[7,2]*m[7,1] + S[2,8]*m[1,8] + S[8,2]*m[8,1] + S[2,9]*m[1,9] + S[9,2]*m[9,1] +
S[2,1]*m[2,1] + S[1,2]*m[1,2] ……………………………………………………………… С99
Пω =
S[9,1]*m[9,1] + S[1,9]*m[1,9] + S[9,2]*m[9,2] + S[2,9]*m[2,9] + S[9,3]*m[9,3] +
S[3,9]*m[3,9] + S[9,4]*m[9,4] + S[4,9]*m[4,9] + S[9,5]*m[9,5] + S[5,9]*m[5,9] +
S[9,6]*m[9,6] + S[6,9]*m[6,9] + S[9,7]*m[9,7] + S[7,9]*m[7,9] +
S[9,8]*m[9,8] + S[8,9]*m[8,9] + S[9,9]*m[9,9] + S[9,9]*m[9,9] +
S[9,9]*m[9,9] + S[9,9]*m[9,9] Получили матрицу С
Пω :
Рисунок
6 Найдём элементы матрицы
Qω по выражению
(4):
Рисунок
7 Получили: min Q= -28
<0 p:=y6=6 , v:=y8=8 è y6:=v=8 , y8:=p=6 и переход к п.3 (т.е. к
Итерации 2) (т.е. у нас y = { 1, 2, 3, 4, 5, 8, 7, 6,
9})
Рисунок
8 Итерация
2: С1
01 =
S[1,1]*m[1,1] + S[1,1]*m[1,1] + S[1,2]*m[1,2] + S[2,1]*m[2,1] +
S[1,3]*m[1,3] + S[3,1]*m[3,1] + S[1,4]*m[1,4] + S[4,1]*m[4,1] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] + S[1,6]*m[1,8] + S[6,1]*m[8,1] + S[1,7]*m[1,7] + S[7,1]*m[7,1] +
S[1,8]*m[1,6] + S[8,1]*m[6,1] + S[1,9]*m[1,9] +
S[9,1]*m[9,1] С2
01 = S[2,1]*m[2,1] +
S[1,2]*m[1,2] + S[2,2]*m[2,2] + S[2,2]*m[2,2] + S[2,3]*m[2,3] +
S[3,2]*m[3,2] + S[2,4]*m[2,4] + S[4,2]*m[4,2] + S[2,5]*m[2,5] +
S[5,2]*m[5,2] + S[2,6]*m[2,8] + S[6,2]*m[8,2] + S[2,7]*m[2,7] + S[7,2]*m[7,2] +
S[2,8]*m[2,6] + S[8,2]*m[6,2] + S[2,9]*m[2,9] +
S[9,2]*m[9,2] С3
01=
S[3,1]*m[3,1] + S[1,3]*m[1,3] + S[3,2]*m[3,2] + S[2,3]*m[2,3] +
S[3,3]*m[3,3] + S[3,3]*m[3,3] + S[3,4]*m[3,4] + S[4,3]*m[4,3] +
S[3,5]*m[3,5] + S[5,3]*m[5,3] + S[3,6]*m[3,8] + S[6,3]*m[8,3] + S[3,7]*m[3,7] +
S[7,3]*m[7,3] + S[3,8]*m[3,6] + S[8,3]*m[6,3] + S[3,9]*m[3,9] +
S[9,3]*m[9,3] С4
01 =
S[4,1]*m[4,1] + S[1,4]*m[1,4] + S[4,2]*m[4,2] + S[2,4]*m[2,4] +
S[4,3]*m[4,3] + S[3,4]*m[3,4] + S[4,4]*m[4,4] + S[4,4]*m[4,4] +
S[4,5]*m[4,5] + S[5,4]*m[5,4] + S[4,6]*m[4,8] + S[6,4]*m[8,4] +
S[4,7]*m[4,7] + S[7,4]*m[7,4] + S[4,8]*m[4,6] + S[8,4]*m[6,4] + S[4,9]*m[4,9] +
S[9,4]*m[9,4] С5
01 =
S[5,1]*m[5,1] + S[1,5]*m[1,5] + S[5,2]*m[5,2] + S[2,5]*m[2,5] + S[5,3]*m[5,3] +
S[3,5]*m[3,5] + S[5,4]*m[5,4] + S[4,5]*m[4,5] + S[5,5]*m[5,5] +
S[5,5]*m[5,5] + S[5,6]*m[5,8] + S[6,5]*m[8,5] + S[5,7]*m[5,7] +
S[7,5]*m[7,5] + S[5,8]*m[5,6] + S[8,5]*m[6,5] + S[5,9]*m[5,9] +
S[9,5]*m[9,5] С6
01 =
S[6,1]*m[8,1] + S[1,6]*m[1,8] + S[6,2]*m[8,2] + S[2,6]*m[2,8] + S[6,3]*m[8,3] +
S[3,6]*m[3,8] + S[6,4]*m[8,4] + S[4,6]*m[4,8] + S[6,5]*m[8,5] +
S[5,6]*m[5,8] + S[6,6]*m[8,8] + S[6,6]*m[8,8] + S[6,7]*m[8,7] +
S[7,6]*m[7,8] + S[6,8]*m[8,6] + S[8,6]*m[6,8] + S[6,9]*m[8,9] +
S[9,6]*m[9,8] С7
01 =
S[7,1]*m[7,1] + S[1,7]*m[1,7] + S[7,2]*m[7,2] + S[2,7]*m[2,7] + S[7,3]*m[7,3] +
S[3,7]*m[3,7] + S[7,4]*m[7,4] + S[4,7]*m[4,7] + S[7,5]*m[7,5] + S[5,7]*m[5,7] +
S[7,6]*m[7,8] + S[6,7]*m[8,7] + S[7,7]*m[7,7] + S[7,7]*m[7,7] +
S[7,8]*m[7,6] + S[8,7]*m[6,7] + S[7,9]*m[7,9] +
S[9,7]*m[9,7] С8
01 =
S[8,1]*m[6,1] + S[1,8]*m[1,6] + S[8,2]*m[6,2] + S[2,8]*m[2,6] + S[8,3]*m[6,3] +
S[3,8]*m[3,6] + S[8,4]*m[6,4] + S[4,8]*m[4,6] + S[8,5]*m[6,5] + S[5,8]*m[5,6] +
S[8,6]*m[6,8] + S[6,8]*m[8,6] + S[8,7]*m[6,7] + S[7,8]*m[7,6] +
S[8,8]*m[6,6] + S[8,8]*m[6,6] + S[8,9]*m[6,9] +
S[9,8]*m[9,6] С9
01 =
S[9,1]*m[9,1] + S[1,9]*m[1,9] + S[9,2]*m[9,2] + S[2,9]*m[2,9] + S[9,3]*m[9,3] +
S[3,9]*m[3,9] + S[9,4]*m[9,4] + S[4,9]*m[4,9] + S[9,5]*m[9,5] + S[5,9]*m[5,9] +
S[9,6]*m[9,8] + S[6,9]*m[8,9] + S[9,7]*m[9,7] + S[7,9]*m[7,9] +
S[9,8]*m[9,6] + S[8,9]*m[6,9] + S[9,9]*m[9,9] +
S[9,9]*m[9,9] С
01
={30, 60, 80, 100, 102, 88, 60 , 104, 80 } С11
Пω
=
S[1,1]*m[1,1] + S[1,1]*m[1,1] + S[1,2]*m[1,2] + S[2,1]*m[2,1] +
S[1,3]*m[1,3] + S[3,1]*m[3,1] + S[1,4]*m[1,4] + S[4,1]*m[4,1] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] + S[1,6]*m[1,8] + S[6,1]*m[8,1] + S[1,7]*m[1,7] + S[7,1]*m[7,1] +
S[1,8]*m[1,6] + S[8,1]*m[6,1] + S[1,9]*m[1,9] + S[9,1]*m[9,1] + S[1,1]*m[1,1] +
S[1,1]*m[1,1] С12
Пω
=
S[1,1]*m[2,1] + S[1,1]*m[1,2] + S[1,2]*m[2,2] + S[2,1]*m[2,2] + S[1,3]*m[2,3] +
S[3,1]*m[3,2] + S[1,4]*m[2,4] + S[4,1]*m[4,2] + S[1,5]*m[2,5] + S[5,1]*m[5,2] +
S[1,6]*m[2,8] + S[6,1]*m[8,2] + S[1,7]*m[2,7] + S[7,1]*m[7,2] + S[1,8]*m[2,6] +
S[8,1]*m[6,2] + S[1,9]*m[2,9] + S[9,1]*m[9,2] + S[1,2]*m[1,2] +
S[2,1]*m[2,1] C13 Пω
= S[1,1]*m[3,1] + S[1,1]*m[1,3] + S[1,2]*m[3,2] + S[2,1]*m[2,3] +
S[1,3]*m[3,3] + S[3,1]*m[3,3] + S[1,4]*m[3,4] + S[4,1]*m[4,3] + S[1,5]*m[3,5] +
S[5,1]*m[5,3] + S[1,6]*m[3,8] + S[6,1]*m[8,3] + S[1,7]*m[3,7] + S[7,1]*m[7,3] +
S[1,8]*m[3,6] + S[8,1]*m[6,3] + S[1,9]*m[3,9] + S[9,1]*m[9,3] + S[1,3]*m[1,3] +
S[3,1]*m[3,1] С14
Пω
=
S[1,1]*m[4,1] + S[1,1]*m[1,4] + S[1,2]*m[4,2] + S[2,1]*m[2,4] +
S[1,3]*m[4,3] + S[3,1]*m[3,4] + S[1,4]*m[4,4] + S[4,1]*m[4,4] + S[1,5]*m[4,5] +
S[5,1]*m[5,4] + S[1,6]*m[4,8] + S[6,1]*m[8,4] + S[1,7]*m[4,7] + S[7,1]*m[7,4] +
S[1,8]*m[4,6] + S[8,1]*m[6,4] + S[1,9]*m[4,9] + S[9,1]*m[9,4] + S[1,4]*m[1,4] +
S[4,1]*m[4,1] С15
Пω =
S[1,1]*m[5,1] + S[1,1]*m[1,5] + S[1,2]*m[5,2] + S[2,1]*m[2,5] +
S[1,3]*m[5,3] + S[3,1]*m[3,5] + S[1,4]*m[5,4] + S[4,1]*m[4,5] + S[1,5]*m[5,5] +
S[5,1]*m[5,5] + S[1,6]*m[5,8] + S[6,1]*m[8,5] + S[1,7]*m[5,7] + S[7,1]*m[7,5] +
S[1,8]*m[5,6] + S[8,1]*m[6,5] + S[1,9]*m[5,9] + S[9,1]*m[9,5] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] С16
Пω =
S[1,1]*m[8,1] + S[1,1]*m[1,8] + S[1,2]*m[8,2] + S[2,1]*m[2,8] +
S[1,3]*m[8,3] + S[3,1]*m[3,8] + S[1,4]*m[8,4] + S[4,1]*m[4,8] + S[1,5]*m[8,5] +
S[5,1]*m[5,8] + S[1,6]*m[8,8] + S[6,1]*m[8,8] + S[1,7]*m[8,7] + S[7,1]*m[7,8] +
S[1,8]*m[8,6] + S[8,1]*m[6,8] + S[1,9]*m[8,9] + S[9,1]*m[9,8] + S[1,6]*m[1,8] +
S[6,1]*m[8,1] С17
Пω =
S[1,1]*m[7,1] + S[1,1]*m[1,7] + S[1,2]*m[7,2] + S[2,1]*m[2,7] +
S[1,3]*m[7,3] + S[3,1]*m[3,7] + S[1,4]*m[7,4] + S[4,1]*m[4,7] + S[1,5]*m[7,5] +
S[5,1]*m[5,7] + S[1,6]*m[7,8] + S[6,1]*m[8,7] + S[1,7]*m[7,7] + S[7,1]*m[7,7] +
S[1,8]*m[7,6] + S[8,1]*m[6,7] + S[1,9]*m[7,9] + S[9,1]*m[9,7] + S[1,7]*m[1,7] +
S[7,1]*m[7,1] С18
Пω =
S[1,1]*m[6,1] + S[1,1]*m[1,6] + S[1,2]*m[6,2] + S[2,1]*m[2,6] +
S[1,3]*m[6,3] + S[3,1]*m[3,6] + S[1,4]*m[6,4] + S[4,1]*m[4,6] + S[1,5]*m[6,5] +
S[5,1]*m[5,6] + S[1,6]*m[6,8] + S[6,1]*m[8,6] + S[1,7]*m[6,7] + S[7,1]*m[7,6] +
S[1,8]*m[6,6] + S[8,1]*m[6,6] + S[1,9]*m[6,9] + S[9,1]*m[9,6] + S[1,8]*m[1,6] +
S[8,1]*m[6,1] С19
Пω
[1,9]= S[1,1]*m[9,1] + S[1,1]*m[1,9] + S[1,2]*m[9,2] +
S[2,1]*m[2,9] + S[1,3]*m[9,3] + S[3,1]*m[3,9] + S[1,4]*m[9,4] +
S[4,1]*m[4,9] + S[1,5]*m[9,5] + S[5,1]*m[5,9] + S[1,6]*m[9,8] + S[6,1]*m[8,9] +
S[1,7]*m[9,7] + S[7,1]*m[7,9] + S[1,8]*m[9,6] + S[8,1]*m[6,9] + S[1,9]*m[9,9] +
S[9,1]*m[9,9] + S[1,9]*m[1,9] + S[9,1]*m[9,1] С21
Пω =
S[2,1]*m[1,1] + S[1,2]*m[1,1] + S[2,2]*m[1,2] + S[2,2]*m[2,1] +
S[2,3]*m[1,3] + S[3,2]*m[3,1] + S[2,4]*m[1,4] + S[4,2]*m[4,1] +
S[2,5]*m[1,5] + S[5,2]*m[5,1] + S[2,6]*m[1,8] + S[6,2]*m[8,1] + S[2,7]*m[1,7] +
S[7,2]*m[7,1] + S[2,8]*m[1,6] + S[8,2]*m[6,1] + S[2,9]*m[1,9] + S[9,2]*m[9,1] +
S[2,1]*m[2,1] + S[1,2]*m[1,2] ……………………………………………………………… С99
Пω =
S[9,1]*m[9,1] + S[1,9]*m[1,9] + S[9,2]*m[9,2] + S[2,9]*m[2,9] + S[9,3]*m[9,3] +
S[3,9]*m[3,9] + S[9,4]*m[9,4] + S[4,9]*m[4,9] + S[9,5]*m[9,5] + S[5,9]*m[5,9] +
S[9,6]*m[9,8] + S[6,9]*m[8,9] + S[9,7]*m[9,7] + S[7,9]*m[7,9] +
S[9,8]*m[9,6] + S[8,9]*m[6,9] + S[9,9]*m[9,9] + S[9,9]*m[9,9] +
S[9,9]*m[9,9] + S[9,9]*m[9,9] Получили матрицу С
Пω :
Рисунок
9 Найдём элементы матрицы
Qω по выражению
(4):
Рисунок
10 Получили: min Q= -10
<0 p:=y2=2 , v:=y3=3 è y2:=v=3 , y3:=p=2 и переход к п.3 (т.е. к
Итерации 2) (т.е. у нас y = { 1, 3, 2, 4, 5, 8, 7, 6,
9})
Рисунок
11 Итерация
3: С1
01 =
S[1,1]*m[1,1] + S[1,1]*m[1,1] + S[1,2]*m[1,3] + S[2,1]*m[3,1] +
S[1,3]*m[1,2] + S[3,1]*m[2,1] + S[1,4]*m[1,4] + S[4,1]*m[4,1] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] + S[1,6]*m[1,8] + S[6,1]*m[8,1] + S[1,7]*m[1,7] + S[7,1]*m[7,1] +
S[1,8]*m[1,6] + S[8,1]*m[6,1] + S[1,9]*m[1,9] +
S[9,1]*m[9,1] С2
01 = S[2,1]*m[3,1] +
S[1,2]*m[1,3] + S[2,2]*m[3,3] + S[2,2]*m[3,3] + S[2,3]*m[3,2] +
S[3,2]*m[2,3] + S[2,4]*m[3,4] + S[4,2]*m[4,3] + S[2,5]*m[3,5] +
S[5,2]*m[5,3] + S[2,6]*m[3,8] + S[6,2]*m[8,3] + S[2,7]*m[3,7] + S[7,2]*m[7,3] +
S[2,8]*m[3,6] + S[8,2]*m[6,3] + S[2,9]*m[3,9] +
S[9,2]*m[9,3] С3
01=
S[3,1]*m[2,1] + S[1,3]*m[1,2] + S[3,2]*m[2,3] + S[2,3]*m[3,2] +
S[3,3]*m[2,2] + S[3,3]*m[2,2] + S[3,4]*m[2,4] + S[4,3]*m[4,2] +
S[3,5]*m[2,5] + S[5,3]*m[5,2] + S[3,6]*m[2,8] + S[6,3]*m[8,2] + S[3,7]*m[2,7] +
S[7,3]*m[7,2] + S[3,8]*m[2,6] + S[8,3]*m[6,2] + S[3,9]*m[2,9] +
S[9,3]*m[9,2] С4
01 =
S[4,1]*m[4,1] + S[1,4]*m[1,4] + S[4,2]*m[4,3] + S[2,4]*m[3,4] +
S[4,3]*m[4,2] + S[3,4]*m[2,4] + S[4,4]*m[4,4] + S[4,4]*m[4,4] +
S[4,5]*m[4,5] + S[5,4]*m[5,4] + S[4,6]*m[4,8] + S[6,4]*m[8,4] +
S[4,7]*m[4,7] + S[7,4]*m[7,4] + S[4,8]*m[4,6] + S[8,4]*m[6,4] + S[4,9]*m[4,9] +
S[9,4]*m[9,4] С5
01 =
S[5,1]*m[5,1] + S[1,5]*m[1,5] + S[5,2]*m[5,3] + S[2,5]*m[3,5] + S[5,3]*m[5,2] +
S[3,5]*m[2,5] + S[5,4]*m[5,4] + S[4,5]*m[4,5] + S[5,5]*m[5,5] +
S[5,5]*m[5,5] + S[5,6]*m[5,8] + S[6,5]*m[8,5] + S[5,7]*m[5,7] +
S[7,5]*m[7,5] + S[5,8]*m[5,6] + S[8,5]*m[6,5] + S[5,9]*m[5,9] +
S[9,5]*m[9,5] С6
01 =
S[6,1]*m[8,1] + S[1,6]*m[1,8] + S[6,2]*m[8,3] + S[2,6]*m[3,8] + S[6,3]*m[8,2] +
S[3,6]*m[2,8] + S[6,4]*m[8,4] + S[4,6]*m[4,8] + S[6,5]*m[8,5] +
S[5,6]*m[5,8] + S[6,6]*m[8,8] + S[6,6]*m[8,8] + S[6,7]*m[8,7] +
S[7,6]*m[7,8] + S[6,8]*m[8,6] + S[8,6]*m[6,8] + S[6,9]*m[8,9] +
S[9,6]*m[9,8] С7
01 =
S[7,1]*m[7,1] + S[1,7]*m[1,7] + S[7,2]*m[7,3] + S[2,7]*m[3,7] + S[7,3]*m[7,2] +
S[3,7]*m[2,7] + S[7,4]*m[7,4] + S[4,7]*m[4,7] + S[7,5]*m[7,5] + S[5,7]*m[5,7] +
S[7,6]*m[7,8] + S[6,7]*m[8,7] + S[7,7]*m[7,7] + S[7,7]*m[7,7] +
S[7,8]*m[7,6] + S[8,7]*m[6,7] + S[7,9]*m[7,9] +
S[9,7]*m[9,7] С8
01 =
S[8,1]*m[6,1] + S[1,8]*m[1,6] + S[8,2]*m[6,3] + S[2,8]*m[3,6] + S[8,3]*m[6,2] +
S[3,8]*m[2,6] + S[8,4]*m[6,4] + S[4,8]*m[4,6] + S[8,5]*m[6,5] + S[5,8]*m[5,6] +
S[8,6]*m[6,8] + S[6,8]*m[8,6] + S[8,7]*m[6,7] + S[7,8]*m[7,6] +
S[8,8]*m[6,6] + S[8,8]*m[6,6] + S[8,9]*m[6,9] +
S[9,8]*m[9,6] С9
01 =
S[9,1]*m[9,1] + S[1,9]*m[1,9] + S[9,2]*m[9,3] + S[2,9]*m[3,9] + S[9,3]*m[9,2] +
S[3,9]*m[2,9] + S[9,4]*m[9,4] + S[4,9]*m[4,9] + S[9,5]*m[9,5] + S[5,9]*m[5,9] +
S[9,6]*m[9,8] + S[6,9]*m[8,9] + S[9,7]*m[9,7] + S[7,9]*m[7,9] +
S[9,8]*m[9,6] + S[8,9]*m[6,9] + S[9,9]*m[9,9] +
S[9,9]*m[9,9] С
01
={48,
78,
52,
72,
102, 88, 60 , 104, 80 } С11
Пω
=
S[1,1]*m[1,1] + S[1,1]*m[1,1] + S[1,2]*m[1,3] + S[2,1]*m[3,1] +
S[1,3]*m[1,2] + S[3,1]*m[2,1] + S[1,4]*m[1,4] + S[4,1]*m[4,1] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] + S[1,6]*m[1,8] + S[6,1]*m[8,1] + S[1,7]*m[1,7] + S[7,1]*m[7,1] +
S[1,8]*m[1,6] + S[8,1]*m[6,1] + S[1,9]*m[1,9] + S[9,1]*m[9,1] + S[1,1]*m[1,1] +
S[1,1]*m[1,1] С12
Пω
=
S[1,1]*m[3,1] + S[1,1]*m[1,3] + S[1,2]*m[3,3] + S[2,1]*m[3,3] + S[1,3]*m[3,2] +
S[3,1]*m[2,3] + S[1,4]*m[3,4] + S[4,1]*m[4,3] + S[1,5]*m[3,5] + S[5,1]*m[5,3] +
S[1,6]*m[3,8] + S[6,1]*m[8,3] + S[1,7]*m[3,7] + S[7,1]*m[7,3] + S[1,8]*m[3,6] +
S[8,1]*m[6,3] + S[1,9]*m[3,9] + S[9,1]*m[9,3] + S[1,2]*m[1,3] +
S[2,1]*m[3,1] C13 Пω
= S[1,1]*m[2,1] + S[1,1]*m[1,2] + S[1,2]*m[2,3] + S[2,1]*m[3,2] +
S[1,3]*m[2,2] + S[3,1]*m[2,2] + S[1,4]*m[2,4] + S[4,1]*m[4,2] + S[1,5]*m[2,5] +
S[5,1]*m[5,2] + S[1,6]*m[2,8] + S[6,1]*m[8,2] + S[1,7]*m[2,7] + S[7,1]*m[7,2] +
S[1,8]*m[2,6] + S[8,1]*m[6,2] + S[1,9]*m[2,9] + S[9,1]*m[9,2] + S[1,3]*m[1,2] +
S[3,1]*m[2,1] С14
Пω
=
S[1,1]*m[4,1] + S[1,1]*m[1,4] + S[1,2]*m[4,3] + S[2,1]*m[3,4] +
S[1,3]*m[4,2] + S[3,1]*m[2,4] + S[1,4]*m[4,4] + S[4,1]*m[4,4] + S[1,5]*m[4,5] +
S[5,1]*m[5,4] + S[1,6]*m[4,8] + S[6,1]*m[8,4] + S[1,7]*m[4,7] + S[7,1]*m[7,4] +
S[1,8]*m[4,6] + S[8,1]*m[6,4] + S[1,9]*m[4,9] + S[9,1]*m[9,4] + S[1,4]*m[1,4] +
S[4,1]*m[4,1] С15
Пω =
S[1,1]*m[5,1] + S[1,1]*m[1,5] + S[1,2]*m[5,3] + S[2,1]*m[3,5] +
S[1,3]*m[5,2] + S[3,1]*m[2,5] + S[1,4]*m[5,4] + S[4,1]*m[4,5] + S[1,5]*m[5,5] +
S[5,1]*m[5,5] + S[1,6]*m[5,8] + S[6,1]*m[8,5] + S[1,7]*m[5,7] + S[7,1]*m[7,5] +
S[1,8]*m[5,6] + S[8,1]*m[6,5] + S[1,9]*m[5,9] + S[9,1]*m[9,5] + S[1,5]*m[1,5] +
S[5,1]*m[5,1] С16
Пω =
S[1,1]*m[8,1] + S[1,1]*m[1,8] + S[1,2]*m[8,3] + S[2,1]*m[3,8] +
S[1,3]*m[8,2] + S[3,1]*m[2,8] + S[1,4]*m[8,4] + S[4,1]*m[4,8] + S[1,5]*m[8,5] +
S[5,1]*m[5,8] + S[1,6]*m[8,8] + S[6,1]*m[8,8] + S[1,7]*m[8,7] + S[7,1]*m[7,8] +
S[1,8]*m[8,6] + S[8,1]*m[6,8] + S[1,9]*m[8,9] + S[9,1]*m[9,8] + S[1,6]*m[1,8] +
S[6,1]*m[8,1] С17
Пω =
S[1,1]*m[7,1] + S[1,1]*m[1,7] + S[1,2]*m[7,3] + S[2,1]*m[3,7] +
S[1,3]*m[7,2] + S[3,1]*m[2,7] + S[1,4]*m[7,4] + S[4,1]*m[4,7] + S[1,5]*m[7,5] +
S[5,1]*m[5,7] + S[1,6]*m[7,8] + S[6,1]*m[8,7] + S[1,7]*m[7,7] + S[7,1]*m[7,7] +
S[1,8]*m[7,6] + S[8,1]*m[6,7] + S[1,9]*m[7,9] + S[9,1]*m[9,7] + S[1,7]*m[1,7] +
S[7,1]*m[7,1] С18
Пω =
S[1,1]*m[6,1] + S[1,1]*m[1,6] + S[1,2]*m[6,3] + S[2,1]*m[3,6] +
S[1,3]*m[6,2] + S[3,1]*m[2,6] + S[1,4]*m[6,4] + S[4,1]*m[4,6] + S[1,5]*m[6,5] +
S[5,1]*m[5,6] + S[1,6]*m[6,8] + S[6,1]*m[8,6] + S[1,7]*m[6,7] + S[7,1]*m[7,6] +
S[1,8]*m[6,6] + S[8,1]*m[6,6] + S[1,9]*m[6,9] + S[9,1]*m[9,6] + S[1,8]*m[1,6] +
S[8,1]*m[6,1] С19
Пω
[1,9]= S[1,1]*m[9,1] + S[1,1]*m[1,9] + S[1,2]*m[9,3] +
S[2,1]*m[3,9] + S[1,3]*m[9,2] + S[3,1]*m[2,9] + S[1,4]*m[9,4] +
S[4,1]*m[4,9] + S[1,5]*m[9,5] + S[5,1]*m[5,9] + S[1,6]*m[9,8] + S[6,1]*m[8,9] +
S[1,7]*m[9,7] + S[7,1]*m[7,9] + S[1,8]*m[9,6] + S[8,1]*m[6,9] + S[1,9]*m[9,9] +
S[9,1]*m[9,9] + S[1,9]*m[1,9] + S[9,1]*m[9,1] С21
Пω =
S[2,1]*m[1,1] + S[1,2]*m[1,1] + S[2,2]*m[1,3] + S[2,2]*m[3,1] +
S[2,3]*m[1,2] + S[3,2]*m[2,1] + S[2,4]*m[1,4] + S[4,2]*m[4,1] +
S[2,5]*m[1,5] + S[5,2]*m[5,1] + S[2,6]*m[1,8] + S[6,2]*m[8,1] + S[2,7]*m[1,7] +
S[7,2]*m[7,1] + S[2,8]*m[1,6] + S[8,2]*m[6,1] + S[2,9]*m[1,9] + S[9,2]*m[9,1] +
S[2,1]*m[3,1] + S[1,2]*m[1,3] ……………………………………………………………… С99
Пω =
S[9,1]*m[9,1] + S[1,9]*m[1,9] + S[9,2]*m[9,3] + S[2,9]*m[3,9] + S[9,3]*m[9,2] +
S[3,9]*m[2,9] + S[9,4]*m[9,4] + S[4,9]*m[4,9] + S[9,5]*m[9,5] + S[5,9]*m[5,9] +
S[9,6]*m[9,8] + S[6,9]*m[8,9] + S[9,7]*m[9,7] + S[7,9]*m[7,9] +
S[9,8]*m[9,6] + S[8,9]*m[6,9] + S[9,9]*m[9,9] + S[9,9]*m[9,9] +
S[9,9]*m[9,9] + S[9,9]*m[9,9] Получили матрицу С
Пω :
Рисунок
12 Найдём элементы матрицы
Qω по выражению
(4):
Рисунок
13 Получили: min Q= 0 ³ 0, следовательно переходим
к п. 12 П. 12 . Корректировка номера исходного
варианта
ω = ω +1 =
2; П. 13
ω£N, значит переходим к п.
2 П. 2 Формирование
для варианта ω исходного списка {yi}ω
y = { 2, 3, 4, 5, 6, 7, 8, 9,
1}
Рисунок
14 П.
3 Итерация
1: С1
02 =
S[1,1]*m[2,2] + S[1,1]*m[2,2] + S[1,2]*m[2,3] + S[2,1]*m[3,2] +
S[1,3]*m[2,4] + S[3,1]*m[4,2] + S[1,4]*m[2,5] + S[4,1]*m[5,2] + S[1,5]*m[2,6] +
S[5,1]*m[6,2] + S[1,6]*m[2,7] + S[6,1]*m[7,2] + S[1,7]*m[2,8] + S[7,1]*m[8,2] +
S[1,8]*m[2,9] + S[8,1]*m[9,2] + S[1,9]*m[2,1] +
S[9,1]*m[1,2] С2
02 = S[2,1]*m[3,2] +
S[1,2]*m[2,3] + S[2,2]*m[3,3] + S[2,2]*m[3,3] + S[2,3]*m[3,4] +
S[3,2]*m[4,3] + S[2,4]*m[3,5] + S[4,2]*m[5,3] + S[2,5]*m[3,6] +
S[5,2]*m[6,3] + S[2,6]*m[3,7] + S[6,2]*m[7,3] + S[2,7]*m[3,8] + S[7,2]*m[8,3] +
S[2,8]*m[3,9] + S[8,2]*m[9,3] + S[2,9]*m[3,1] +
S[9,2]*m[1,3] С3
02=
S[3,1]*m[4,2] + S[1,3]*m[2,4] + S[3,2]*m[4,3] + S[2,3]*m[3,4] +
S[3,3]*m[4,4] + S[3,3]*m[4,4] + S[3,4]*m[4,5] + S[4,3]*m[5,4] +
S[3,5]*m[4,6] + S[5,3]*m[6,4] + S[3,6]*m[4,7] + S[6,3]*m[7,4] + S[3,7]*m[4,8] +
S[7,3]*m[8,4] + S[3,8]*m[4,9] + S[8,3]*m[9,4] + S[3,9]*m[4,1] +
S[9,3]*m[1,4] С4
02 =
S[4,1]*m[5,2] + S[1,4]*m[2,5] + S[4,2]*m[5,3] + S[2,4]*m[3,5] +
S[4,3]*m[5,4] + S[3,4]*m[4,5] + S[4,4]*m[5,5] + S[4,4]*m[5,5] +
S[4,5]*m[5,6] + S[5,4]*m[6,5] + S[4,6]*m[5,7] + S[6,4]*m[7,5] +
S[4,7]*m[5,8] + S[7,4]*m[8,5] + S[4,8]*m[5,9] + S[8,4]*m[9,5] + S[4,9]*m[5,1] +
S[9,4]*m[1,5] С5
02 =
S[5,1]*m[6,2] + S[1,5]*m[2,6] + S[5,2]*m[6,3] + S[2,5]*m[3,6] + S[5,3]*m[6,4] +
S[3,5]*m[4,6] + S[5,4]*m[6,5] + S[4,5]*m[5,6] + S[5,5]*m[6,6] +
S[5,5]*m[6,6] + S[5,6]*m[6,7] + S[6,5]*m[7,6] + S[5,7]*m[6,8] +
S[7,5]*m[8,6] + S[5,8]*m[6,9] + S[8,5]*m[9,6] + S[5,9]*m[6,1] +
S[9,5]*m[1,6] С6
02 =
S[6,1]*m[7,2] + S[1,6]*m[2,7] + S[6,2]*m[7,3] + S[2,6]*m[3,7] + S[6,3]*m[7,4] +
S[3,6]*m[4,7] + S[6,4]*m[7,5] + S[4,6]*m[5,7] + S[6,5]*m[7,6] +
S[5,6]*m[6,7] + S[6,6]*m[7,7] + S[6,6]*m[7,7] + S[6,7]*m[7,8] +
S[7,6]*m[8,7] + S[6,8]*m[7,9] + S[8,6]*m[9,7] + S[6,9]*m[7,1] +
S[9,6]*m[1,7] С7
02 =
S[7,1]*m[8,2] + S[1,7]*m[2,8] + S[7,2]*m[8,3] + S[2,7]*m[3,8] + S[7,3]*m[8,4] +
S[3,7]*m[4,8] + S[7,4]*m[8,5] + S[4,7]*m[5,8] + S[7,5]*m[8,6] + S[5,7]*m[6,8] +
S[7,6]*m[8,7] + S[6,7]*m[7,8] + S[7,7]*m[8,8] + S[7,7]*m[8,8] +
S[7,8]*m[8,9] + S[8,7]*m[9,8] + S[7,9]*m[8,1] +
S[9,7]*m[1,8] С8
02 =
S[8,1]*m[9,2] + S[1,8]*m[2,9] + S[8,2]*m[9,3] + S[2,8]*m[3,9] + S[8,3]*m[9,4] +
S[3,8]*m[4,9] + S[8,4]*m[9,5] + S[4,8]*m[5,9] + S[8,5]*m[9,6] + S[5,8]*m[6,9] +
S[8,6]*m[9,7] + S[6,8]*m[7,9] + S[8,7]*m[9,8] + S[7,8]*m[8,9] +
S[8,8]*m[9,9] + S[8,8]*m[9,9] + S[8,9]*m[9,1] +
S[9,8]*m[1,9] С9
02 =
S[9,1]*m[1,2] + S[1,9]*m[2,1] + S[9,2]*m[1,3] + S[2,9]*m[3,1] + S[9,3]*m[1,4] +
S[3,9]*m[4,1] + S[9,4]*m[1,5] + S[4,9]*m[5,1] + S[9,5]*m[1,6] + S[5,9]*m[6,1] +
S[9,6]*m[1,7] + S[6,9]*m[7,1] + S[9,7]*m[1,8] + S[7,9]*m[8,1] +
S[9,8]*m[1,9] + S[8,9]*m[9,1] + S[9,9]*m[1,1] +
S[9,9]*m[1,1] С
02
={30, 80, 100, 130, 104, 60, 116, 280, 200} П.
4 С11
Пω
=
S[1,1]*m[2,2] + S[1,1]*m[2,2] + S[1,2]*m[2,3] + S[2,1]*m[3,2] +
S[1,3]*m[2,4] + S[3,1]*m[4,2] + S[1,4]*m[2,5] + S[4,1]*m[5,2] + S[1,5]*m[2,6] +
S[5,1]*m[6,2] + S[1,6]*m[2,7] + S[6,1]*m[7,2] + S[1,7]*m[2,8] + S[7,1]*m[8,2] +
S[1,8]*m[2,9] + S[8,1]*m[9,2] + S[1,9]*m[2,1] + S[9,1]*m[1,2] + S[1,1]*m[2,2] +
S[1,1]*m[2,2] С12
Пω
=
S[1,1]*m[3,2] + S[1,1]*m[2,3] + S[1,2]*m[3,3] + S[2,1]*m[3,3] + S[1,3]*m[3,4] +
S[3,1]*m[4,3] + S[1,4]*m[3,5] + S[4,1]*m[5,3] + S[1,5]*m[3,6] + S[5,1]*m[6,3] +
S[1,6]*m[3,7] + S[6,1]*m[7,3] + S[1,7]*m[3,8] + S[7,1]*m[8,3] + S[1,8]*m[3,9] +
S[8,1]*m[9,3] + S[1,9]*m[3,1] + S[9,1]*m[1,3] + S[1,2]*m[2,3] +
S[2,1]*m[3,2] C13 Пω
= S[1,1]*m[4,2] + S[1,1]*m[2,4] + S[1,2]*m[4,3] + S[2,1]*m[3,4] +
S[1,3]*m[4,4] + S[3,1]*m[4,4] + S[1,4]*m[4,5] + S[4,1]*m[5,4] + S[1,5]*m[4,6] +
S[5,1]*m[6,4] + S[1,6]*m[4,7] + S[6,1]*m[7,4] + S[1,7]*m[4,8] + S[7,1]*m[8,4] +
S[1,8]*m[4,9] + S[8,1]*m[9,4] + S[1,9]*m[4,1] + S[9,1]*m[1,4] + S[1,3]*m[2,4] +
S[3,1]*m[4,2] С14
Пω
=
S[1,1]*m[5,2] + S[1,1]*m[2,5] + S[1,2]*m[5,3] + S[2,1]*m[3,5] +
S[1,3]*m[5,4] + S[3,1]*m[4,5] + S[1,4]*m[5,5] + S[4,1]*m[5,5] + S[1,5]*m[5,6] +
S[5,1]*m[6,5] + S[1,6]*m[5,7] + S[6,1]*m[7,5] + S[1,7]*m[5,8] + S[7,1]*m[8,5] +
S[1,8]*m[5,9] + S[8,1]*m[9,5] + S[1,9]*m[5,1] + S[9,1]*m[1,5] + S[1,4]*m[2,5] +
S[4,1]*m[5,2] С15
Пω =
S[1,1]*m[6,2] + S[1,1]*m[2,6] + S[1,2]*m[6,3] + S[2,1]*m[3,6] +
S[1,3]*m[6,4] + S[3,1]*m[4,6] + S[1,4]*m[6,5] + S[4,1]*m[5,6] + S[1,5]*m[6,6] +
S[5,1]*m[6,6] + S[1,6]*m[6,7] + S[6,1]*m[7,6] + S[1,7]*m[6,8] + S[7,1]*m[8,6] +
S[1,8]*m[6,9] + S[8,1]*m[9,6] + S[1,9]*m[6,1] + S[9,1]*m[1,6] + S[1,5]*m[2,6] +
S[5,1]*m[6,2] С16
Пω =
S[1,1]*m[7,2] + S[1,1]*m[2,7] + S[1,2]*m[7,3] + S[2,1]*m[3,7] +
S[1,3]*m[7,4] + S[3,1]*m[4,7] + S[1,4]*m[7,5] + S[4,1]*m[5,7] + S[1,5]*m[7,6] +
S[5,1]*m[6,7] + S[1,6]*m[7,7] + S[6,1]*m[7,7] + S[1,7]*m[7,8] + S[7,1]*m[8,7] +
S[1,8]*m[7,9] + S[8,1]*m[9,7] + S[1,9]*m[7,1] + S[9,1]*m[1,7] + S[1,6]*m[2,7] +
S[6,1]*m[7,2] С17
Пω =
S[1,1]*m[8,2] + S[1,1]*m[2,8] + S[1,2]*m[8,3] + S[2,1]*m[3,8] +
S[1,3]*m[8,4] + S[3,1]*m[4,8] + S[1,4]*m[8,5] + S[4,1]*m[5,8] + S[1,5]*m[8,6] +
S[5,1]*m[6,8] + S[1,6]*m[8,7] + S[6,1]*m[7,8] + S[1,7]*m[8,8] + S[7,1]*m[8,8] +
S[1,8]*m[8,9] + S[8,1]*m[9,8] + S[1,9]*m[8,1] + S[9,1]*m[1,8] + S[1,7]*m[2,8] +
S[7,1]*m[8,2] С18
Пω =
S[1,1]*m[9,2] + S[1,1]*m[2,9] + S[1,2]*m[9,3] + S[2,1]*m[3,9] +
S[1,3]*m[9,4] + S[3,1]*m[4,9] + S[1,4]*m[9,5] + S[4,1]*m[5,9] + S[1,5]*m[9,6] +
S[5,1]*m[6,9] + S[1,6]*m[9,7] + S[6,1]*m[7,9] + S[1,7]*m[9,8] + S[7,1]*m[8,9] +
S[1,8]*m[9,9] + S[8,1]*m[9,9] + S[1,9]*m[9,1] + S[9,1]*m[1,9] + S[1,8]*m[2,9] +
S[8,1]*m[9,2] С19
Пω
[1,9]= S[1,1]*m[1,2] + S[1,1]*m[2,1] + S[1,2]*m[1,3] +
S[2,1]*m[3,1] + S[1,3]*m[1,4] + S[3,1]*m[4,1] + S[1,4]*m[1,5] +
S[4,1]*m[5,1] + S[1,5]*m[1,6] + S[5,1]*m[6,1] + S[1,6]*m[1,7] + S[6,1]*m[7,1] +
S[1,7]*m[1,8] + S[7,1]*m[8,1] + S[1,8]*m[1,9] + S[8,1]*m[9,1] + S[1,9]*m[1,1] +
S[9,1]*m[1,1] + S[1,9]*m[2,1] + S[9,1]*m[1,2] С21
Пω =
S[2,1]*m[2,2] + S[1,2]*m[2,2] + S[2,2]*m[2,3] + S[2,2]*m[3,2] +
S[2,3]*m[2,4] + S[3,2]*m[4,2] + S[2,4]*m[2,5] + S[4,2]*m[5,2] +
S[2,5]*m[2,6] + S[5,2]*m[6,2] + S[2,6]*m[2,7] + S[6,2]*m[7,2] + S[2,7]*m[2,8] +
S[7,2]*m[8,2] + S[2,8]*m[2,9] + S[8,2]*m[9,2] + S[2,9]*m[2,1] + S[9,2]*m[1,2] +
S[2,1]*m[3,2] + S[1,2]*m[2,3] ……………………………………………………………… С99
Пω =
S[9,1]*m[1,2] + S[1,9]*m[2,1] + S[9,2]*m[1,3] + S[2,9]*m[3,1] + S[9,3]*m[1,4] +
S[3,9]*m[4,1] + S[9,4]*m[1,5] + S[4,9]*m[5,1] + S[9,5]*m[1,6] + S[5,9]*m[6,1] +
S[9,6]*m[1,7] + S[6,9]*m[7,1] + S[9,7]*m[1,8] + S[7,9]*m[8,1] +
S[9,8]*m[1,9] + S[8,9]*m[9,1] + S[9,9]*m[1,1] + S[9,9]*m[1,1] +
S[9,9]*m[1,1] + S[9,9]*m[1,1] Получили матрицу С
Пω :
Рисунок
15 Найдём элементы матрицы
Qω по выражению
(4):
Рисунок
16 Получили: min Q= -60
<0 p:=y7=8 , v:=y8=9 è y7:=v=9 , y8:=p=8 и переход к п.3 (т.е. к
Итерации 2) (т.е. у нас y = { 2, 3, 4, 5, 6, 7, 9, 8,
1})
Рисунок
17 Итерация
2: С1
02 =
S[1,1]*m[2,2] + S[1,1]*m[2,2] + S[1,2]*m[2,3] + S[2,1]*m[3,2] +
S[1,3]*m[2,4] + S[3,1]*m[4,2] + S[1,4]*m[2,5] + S[4,1]*m[5,2] + S[1,5]*m[2,6] +
S[5,1]*m[6,2] + S[1,6]*m[2,7] + S[6,1]*m[7,2] + S[1,7]*m[2,9] + S[7,1]*m[9,2] +
S[1,8]*m[2,8] + S[8,1]*m[8,2] + S[1,9]*m[2,1] +
S[9,1]*m[1,2] С2
02 = S[2,1]*m[3,2] +
S[1,2]*m[2,3] + S[2,2]*m[3,3] + S[2,2]*m[3,3] + S[2,3]*m[3,4] +
S[3,2]*m[4,3] + S[2,4]*m[3,5] + S[4,2]*m[5,3] + S[2,5]*m[3,6] +
S[5,2]*m[6,3] + S[2,6]*m[3,7] + S[6,2]*m[7,3] + S[2,7]*m[3,9] + S[7,2]*m[9,3] +
S[2,8]*m[3,8] + S[8,2]*m[8,3] + S[2,9]*m[3,1] +
S[9,2]*m[1,3] С3
02=
S[3,1]*m[4,2] + S[1,3]*m[2,4] + S[3,2]*m[4,3] + S[2,3]*m[3,4] +
S[3,3]*m[4,4] + S[3,3]*m[4,4] + S[3,4]*m[4,5] + S[4,3]*m[5,4] +
S[3,5]*m[4,6] + S[5,3]*m[6,4] + S[3,6]*m[4,7] + S[6,3]*m[7,4] + S[3,7]*m[4,9] +
S[7,3]*m[9,4] + S[3,8]*m[4,8] + S[8,3]*m[8,4] + S[3,9]*m[4,1] +
S[9,3]*m[1,4] С4
02 =
S[4,1]*m[5,2] + S[1,4]*m[2,5] + S[4,2]*m[5,3] + S[2,4]*m[3,5] +
S[4,3]*m[5,4] + S[3,4]*m[4,5] + S[4,4]*m[5,5] + S[4,4]*m[5,5] +
S[4,5]*m[5,6] + S[5,4]*m[6,5] + S[4,6]*m[5,7] + S[6,4]*m[7,5] +
S[4,7]*m[5,9] + S[7,4]*m[9,5] + S[4,8]*m[5,8] + S[8,4]*m[8,5] + S[4,9]*m[5,1] +
S[9,4]*m[1,5] С5
02 =
S[5,1]*m[6,2] + S[1,5]*m[2,6] + S[5,2]*m[6,3] + S[2,5]*m[3,6] + S[5,3]*m[6,4] +
S[3,5]*m[4,6] + S[5,4]*m[6,5] + и +
S[5,5]*m[6,6] + S[5,5]*m[6,6] + S[5,6]*m[6,7] + S[6,5]*m[7,6] +
S[5,7]*m[6,9] + S[7,5]*m[9,6] + S[5,8]*m[6,8] + S[8,5]*m[8,6] + S[5,9]*m[6,1] +
S[9,5]*m[1,6] С6
02 =
S[6,1]*m[7,2] + S[1,6]*m[2,7] + S[6,2]*m[7,3] + S[2,6]*m[3,7] + S[6,3]*m[7,4] +
S[3,6]*m[4,7] + S[6,4]*m[7,5] + S[4,6]*m[5,7] + S[6,5]*m[7,6] +
S[5,6]*m[6,7] + S[6,6]*m[7,7] + S[6,6]*m[7,7] + S[6,7]*m[7,9] +
S[7,6]*m[9,7] + S[6,8]*m[7,8] + S[8,6]*m[8,7] + S[6,9]*m[7,1] +
S[9,6]*m[1,7] С7
02 =
S[7,1]*m[9,2] + S[1,7]*m[2,9] + S[7,2]*m[9,3] + S[2,7]*m[3,9] + S[7,3]*m[9,4] +
S[3,7]*m[4,9] + S[7,4]*m[9,5] + S[4,7]*m[5,9] + S[7,5]*m[9,6] + S[5,7]*m[6,9] +
S[7,6]*m[9,7] + S[6,7]*m[7,9] + S[7,7]*m[9,9] + S[7,7]*m[9,9] +
S[7,8]*m[9,8] + S[8,7]*m[8,9] + S[7,9]*m[9,1] +
S[9,7]*m[1,9] С8
02 =
S[8,1]*m[8,2] + S[1,8]*m[2,8] + S[8,2]*m[8,3] + S[2,8]*m[3,8] + S[8,3]*m[8,4] +
S[3,8]*m[4,8] + S[8,4]*m[8,5] + S[4,8]*m[5,8] + S[8,5]*m[8,6] + S[5,8]*m[6,8] +
S[8,6]*m[8,7] + S[6,8]*m[7,8] + S[8,7]*m[8,9] + S[7,8]*m[9,8] +
S[8,8]*m[8,8] + S[8,8]*m[8,8] + S[8,9]*m[8,1] +
S[9,8]*m[1,8] С9
02 =
S[9,1]*m[1,2] + S[1,9]*m[2,1] + S[9,2]*m[1,3] + S[2,9]*m[3,1] + S[9,3]*m[1,4] +
S[3,9]*m[4,1] + S[9,4]*m[1,5] + S[4,9]*m[5,1] + S[9,5]*m[1,6] + S[5,9]*m[6,1] +
S[9,6]*m[1,7] + S[6,9]*m[7,1] + S[9,7]*m[1,9] + S[7,9]*m[9,1] +
S[9,8]*m[1,8] + S[8,9]*m[8,1] + S[9,9]*m[1,1] +
S[9,9]*m[1,1] С
02 ={
30,
80,
100,
130,
104,
80,
136,
200,
120} П.
4 С11
Пω
=
S[1,1]*m[2,2] + S[1,1]*m[2,2] + S[1,2]*m[2,3] + S[2,1]*m[3,2] +
S[1,3]*m[2,4] + S[3,1]*m[4,2] + S[1,4]*m[2,5] + S[4,1]*m[5,2] + S[1,5]*m[2,6] +
S[5,1]*m[6,2] + S[1,6]*m[2,7] + S[6,1]*m[7,2] + S[1,7]*m[2,9] + S[7,1]*m[9,2] +
S[1,8]*m[2,8] + S[8,1]*m[8,2] + S[1,9]*m[2,1] + S[9,1]*m[1,2] + S[1,1]*m[2,2] +
S[1,1]*m[2,2] С12
Пω
=
S[1,1]*m[3,2] + S[1,1]*m[2,3] + S[1,2]*m[3,3] + S[2,1]*m[3,3] + S[1,3]*m[3,4] +
S[3,1]*m[4,3] + S[1,4]*m[3,5] + S[4,1]*m[5,3] + S[1,5]*m[3,6] + S[5,1]*m[6,3] +
S[1,6]*m[3,7] + S[6,1]*m[7,3] + S[1,7]*m[3,9] + S[7,1]*m[9,3] + S[1,8]*m[3,8] +
S[8,1]*m[8,3] + S[1,9]*m[3,1] + S[9,1]*m[1,3] + S[1,2]*m[2,3] +
S[2,1]*m[3,2] C13 Пω
= S[1,1]*m[4,2] + S[1,1]*m[2,4] + S[1,2]*m[4,3] + S[2,1]*m[3,4] +
S[1,3]*m[4,4] + S[3,1]*m[4,4] + S[1,4]*m[4,5] + S[4,1]*m[5,4] + S[1,5]*m[4,6] +
S[5,1]*m[6,4] + S[1,6]*m[4,7] + S[6,1]*m[7,4] + S[1,7]*m[4,9] + S[7,1]*m[9,4] +
S[1,8]*m[4,8] + S[8,1]*m[8,4] + S[1,9]*m[4,1] + S[9,1]*m[1,4] + S[1,3]*m[2,4] +
S[3,1]*m[4,2] С14
Пω
=
S[1,1]*m[5,2] + S[1,1]*m[2,5] + S[1,2]*m[5,3] + S[2,1]*m[3,5] +
S[1,3]*m[5,4] + S[3,1]*m[4,5] + S[1,4]*m[5,5] + S[4,1]*m[5,5] + S[1,5]*m[5,6] +
S[5,1]*m[6,5] + S[1,6]*m[5,7] + S[6,1]*m[7,5] + S[1,7]*m[5,9] + S[7,1]*m[9,5] +
S[1,8]*m[5,8] + S[8,1]*m[8,5] + S[1,9]*m[5,1] + S[9,1]*m[1,5] + S[1,4]*m[2,5] +
S[4,1]*m[5,2] С15
Пω =
S[1,1]*m[6,2] + S[1,1]*m[2,6] + S[1,2]*m[6,3] + S[2,1]*m[3,6] +
S[1,3]*m[6,4] + S[3,1]*m[4,6] + S[1,4]*m[6,5] + S[4,1]*m[5,6] + S[1,5]*m[6,6] +
S[5,1]*m[6,6] + S[1,6]*m[6,7] + S[6,1]*m[7,6] + S[1,7]*m[6,9] + S[7,1]*m[9,6] +
S[1,8]*m[6,8] + S[8,1]*m[8,6] + S[1,9]*m[6,1] + S[9,1]*m[1,6] + S[1,5]*m[2,6] +
S[5,1]*m[6,2] С16
Пω =
S[1,1]*m[7,2] + S[1,1]*m[2,7] + S[1,2]*m[7,3] + S[2,1]*m[3,7] +
S[1,3]*m[7,4] + S[3,1]*m[4,7] + S[1,4]*m[7,5] + S[4,1]*m[5,7] + S[1,5]*m[7,6] +
S[5,1]*m[6,7] + S[1,6]*m[7,7] + S[6,1]*m[7,7] + S[1,7]*m[7,9] + S[7,1]*m[9,7] +
S[1,8]*m[7,8] + S[8,1]*m[8,7] + S[1,9]*m[7,1] + S[9,1]*m[1,7] + S[1,6]*m[2,7] +
S[6,1]*m[7,2] С17
Пω =
S[1,1]*m[9,2] + S[1,1]*m[2,9] + S[1,2]*m[9,3] + S[2,1]*m[3,9] +
S[1,3]*m[9,4] + S[3,1]*m[4,9] + S[1,4]*m[9,5] + S[4,1]*m[5,9] + S[1,5]*m[9,6] +
S[5,1]*m[6,9] + S[1,6]*m[9,7] + S[6,1]*m[7,9] + S[1,7]*m[9,9] + S[7,1]*m[9,9] +
S[1,8]*m[9,8] + S[8,1]*m[8,9] + S[1,9]*m[9,1] + S[9,1]*m[1,9] + S[1,7]*m[2,9] +
S[7,1]*m[9,2] С18
Пω =
S[1,1]*m[8,2] + S[1,1]*m[2,8] + S[1,2]*m[8,3] + S[2,1]*m[3,8] +
S[1,3]*m[8,4] + S[3,1]*m[4,8] + S[1,4]*m[8,5] + S[4,1]*m[5,8] + S[1,5]*m[8,6] +
S[5,1]*m[6,8] + S[1,6]*m[8,7] + S[6,1]*m[7,8] + S[1,7]*m[8,9] + S[7,1]*m[9,8] +
S[1,8]*m[8,8] + S[8,1]*m[8,8] + S[1,9]*m[8,1] + S[9,1]*m[1,8] + S[1,8]*m[2,8] +
S[8,1]*m[8,2] С19
Пω
S[1,1]*m[1,2] + S[1,1]*m[2,1] + S[1,2]*m[1,3] + S[2,1]*m[3,1] +
S[1,3]*m[1,4] + S[3,1]*m[4,1] + S[1,4]*m[1,5] + S[4,1]*m[5,1] + S[1,5]*m[1,6] +
S[5,1]*m[6,1] + S[1,6]*m[1,7] + S[6,1]*m[7,1] + S[1,7]*m[1,9] + S[7,1]*m[9,1] +
S[1,8]*m[1,8] + S[8,1]*m[8,1] + S[1,9]*m[1,1] + S[9,1]*m[1,1] + S[1,9]*m[2,1] +
S[9,1]*m[1,2] С21
Пω =
S[2,1]*m[2,2] + S[1,2]*m[2,2] + S[2,2]*m[2,3] + S[2,2]*m[3,2] +
S[2,3]*m[2,4] + S[3,2]*m[4,2] + S[2,4]*m[2,5] + S[4,2]*m[5,2] +
S[2,5]*m[2,6] + S[5,2]*m[6,2] + S[2,6]*m[2,7] + S[6,2]*m[7,2] + S[2,7]*m[2,9] +
S[7,2]*m[9,2] + S[2,8]*m[2,8] + S[8,2]*m[8,2] + S[2,9]*m[2,1] + S[9,2]*m[1,2] +
S[2,1]*m[3,2] + S[1,2]*m[2,3] ……………………………………………………………… С99
Пω =
S[9,1]*m[1,2] + S[1,9]*m[2,1] + S[9,2]*m[1,3] + S[2,9]*m[3,1] + S[9,3]*m[1,4] +
S[3,9]*m[4,1] + S[9,4]*m[1,5] + S[4,9]*m[5,1] + S[9,5]*m[1,6] + S[5,9]*m[6,1] +
S[9,6]*m[1,7] + S[6,9]*m[7,1] + S[9,7]*m[1,9] + S[7,9]*m[9,1] +
S[9,8]*m[1,8] + S[8,9]*m[8,1] + S[9,9]*m[1,1] + S[9,9]*m[1,1] +
S[9,9]*m[1,1] + S[9,9]*m[1,1] Получили матрицу С
Пω :
Рисунок
18 дём
элементы матрицы Qω по выражению
(4):
Рисунок
19 Получили: min Q= -28
<0 p:=y1=2 , v:=y2=3 è y1:=v=3 , y2:=p=2 и переход к п.3 (т.е. к
Итерации 3) (т.е. у нас y = { 3, 2, 4, 5, 6, 7, 9, 8,
1})
Рисунок
20 Все промежуточные
результаты, иллюстрирующие основные промежуточные значения для всех итераций и
вариантов ω=1…9 (по алгоритму), приведены в таблице рисунка
21.
Рисунок
21 П. 14. Вывод результатов
расчёта оптимального значения целевой функции Q0 и списка оптимальных
решений {yi}*: Получили несколько вариантов с одинаковыми значениями целевых функцийQ0 =
342
{9, 6, 7, 8, 5, 4, 2, 3, 1}
(вариант 5
) {yi}* = {9, 7, 6,
8, 5, 4, 2, 3, 1} (вариант 6
)
{1, 3, 2, 4, 5, 8, 7, 6, 9}
(вариант 1 )
{3, 1, 2, 4, 5, 8, 6, 7, 9}
(вариант 9
) Принимаем в качестве решения
вариант 1
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