![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAACCAYAAACOoybuAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAYSURBVBjTY2BgYNgPxP+JwPsZGhsbicYAMTcbF7agdqcAAAAASUVORK5CYII=)
Вычислительной схеме модифицированного симплекс-метода соответствует система таблиц
T1 и
Т2(q). Таблица
T1 (
рис. 1.7) является общей для всех итераций и служит для получениястроки оценок текущего базисного плана
a0(β
(q)). Если обозначить через δ
i(β
(q)) (
i Î 0 :
m) строки матрицы Δ
-1(β
(q)), то из (1.26), в частности, следует, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAACCAYAAABsfz2XAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAaSURBVBjTY2hsbGQAgv1A/J8IvJ8BpIEUDAAzTx4dyM8EPQAAAABJRU5ErkJggg==)
Как видно из
рис. 1.7,
T1 состоит из трех блоков:
-
в центре содержится матрицаА;
-
в левом блоке таблицы на каждой итерации дописываются нулевые строки матрицы Δ
-1(β
(q))
для текущего базиса;
- нижний блок, расположенный под матрицейА, на каждой итерации дополняется строкой оценок текущего плана, вычисленной по формуле (1.42).
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAACCAYAAAC3xJe1AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAbSURBVBjTY2BgYNgPxP+phPc3NjYyMIAIamMAkag0rwbBQu0AAAAASUVORK5CYII=)
Симплекс-таблица
Т2(q), изображенная на
рис. 1.8, соответствует допустимому базису КЗЛП β
(q), получаемому на
q-й итерации. Столбец
N(β
(q)) содержит номера базисных столбцов (в последовательности вхождения в базис); столбец
b(β
(q)) — компоненты вектора ограничений относительно текущего базиса β
(q); Δ
-1(β
(q)) — матрица, обратная по отношению к матрице расширенных столбцов текущего базиса β
(q); графа
аl содержит расширенный вектор условий, вводимый в базис на текущей итерации, а следующая графа — координаты
аl(β
(q))этого же столбца в текущем базисе β
(q).
![](data:image/png;base64,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)
По аналогии с п. 1.4.1 опишем формальную схему алгоритма модифицированного симплекс-метода.
0-этап. Нахождение допустимого базисного плана.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAACCAYAAABsfz2XAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAZSURBVBjTY2hsbGQgBUMIBob9QPyfCLwfAGHKHh0v/IWnAAAAAElFTkSuQmCC)
1. Для поиска допустимого базиса может быть применен метод минимизации невязок, рассмотренный в п. 1.4.5. При этом для решения вспомогательной задачи используется процедурамодифицированного симплекс-метода. В результате 0-этапа мы получаем допустимый базисный план
x(β
(1)) и соответствующие ему матрицу Δ
-1(β
(1))и вектор
b(β
(1)).
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAACCAYAAACOoybuAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAYSURBVBjTY2BgYNgPxP+JwPsZGhsbicYAMTcbF7agdqcAAAAASUVORK5CYII=)
2. Заполняем центральную часть таблицы
T1, содержащую матрицу
А.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABUAAAACCAYAAAC3xJe1AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAaSURBVBjTY2hsbGQAgv1A/J9KeD8DyFBqYwC86DSvpShIDAAAAABJRU5ErkJggg==)
3. Содержимое матрицы Δ
-1(β
(1))и вектора
b(β
(1)), полученных на этапе поиска допустимого базисного плана, переносится в таблицу
T2(1).
4. Полагаем номер текущей итерацииq равным 1 и переходим к I-этапу.
1-этап. Стандартная итерация алгоритма — выполняется для очередного базисного плана x(β(q)).
1°. Проверка оптимальности текущего базисного плана. Содержимое нулевой строки таблицы T2(q) — δ0(β(q)) переписывается в соответствующую графу таблицы T1. По формуле (1.42) рассчитываем и заполняем строку a0(β(q)). Осуществляем просмотр строки оценок a0(β(q)). Возможны два варианта:
1΄. a0(β(q))≥0 —план, соответствующий текущему базису задачи, оптимален. Вычислительный процесс закончен. Согласно формулам (1.33) и (1.32) выписываются оптимальный план задачи х* =x(β(q)) и оптимальное значение целевой функцииf(х*)=f(x(β(q))).
1". В строке оценок a0(β(q))существует по меньшей мере один элемент a0,j(β(q))<0, т. е. имеющий отрицательную оценку. Следовательно, план x(β(q)) —неоптимален. Выбирается номер l, соответствующий элементу, имеющему минимальную (максимальную по абсолютной величине) отрицательную оценку:
l-й столбец матрицы
A становится
ведущим и должен быть введен в очередной базис. Переходим к пункту 2° алгоритма.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAACCAYAAABsfz2XAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAbSURBVBjTY2hsbGQgBUMIBob9QPyfAN4PUgsAZFQeoZBtxrEAAAAASUVORK5CYII=)
2°.
Определение столбца, выводимого из базиса. Переписываем ведущий столбец
аl из таблицы
T1 в текущую таблицу
Т2(q). По формуле
аl(β
(q)) = Δ
-1(β
(q))
аl заполняем соответствующий столбец в таблице
Т2(q). Возможны два варианта:
2'. Для всехiÎ 1: mаi,l(β(q))≤0. Делается вывод о неограниченности целевой функции и завершается вычислительный процесс.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAACCAYAAABc8yy2AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAbSURBVBjTY2hsbGSgBYYQDAz7gfg/lfB+kJkANas3tXjgkoUAAAAASUVORK5CYII=)
2". Существует по крайней мере один индекс
iÎ 1:
m, для которого
аi,l(β
(q))>0. Согласно правилу (1.27) определяются место
r и номер
Nr(β
(q)) для столбца, выводимого из базиса. Переходим к пункту 3° алгоритма.
3°. Пересчет относительно нового базиса элементов столбца bи матрицыΔ-1. Переход к новому базисуβ(q+1), который получается введением в базис β(q) столбца аl и выводом из него столбца аr, осуществляется по формулам, аналогичным формулам (1.28)-(1.31). Они имеют вид:
![](data:image/png;base64,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)
Полагаем номер текущей итерацииq: =q+l и переходим к первому пункту алгоритма.
В завершение подчеркнем, что в силу приведенных выше преимуществ именно модифицированный симплекс-метод реально применяется в программном обеспечении, предназначенном для решения канонических задач линейного программирования.
1.5.2. Пример решения ЗЛП модифицированным симплекс-методом. Приведем решение рассмотренной ранее задачи (1.34)-(1.35), основанное на использовании процедуры модифицированного симплекс-метода. По аналогии с п. 1.4.3оно начинается с выбора очевидного исходного базиса, образуемого столбцами {5,2,3}. Для него уже были вычислены Δ-1(β(q)) и b(β(q)), поэтому заполнение начальных таблиц T1 и Т2(1) не представляет труда.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAACCAYAAABsfz2XAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAaSURBVBjTY2hsbGQAgv1A/J8A3g9WCyJIwQBPHR6hDqBwBAAAAABJRU5ErkJggg==)
На первой итерации мы переписываем нулевую строку
из Т2(1) вT1 и, умножив ее на матрицу A, получаем строку оценок
![](data:image/png;base64,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)
Так какa0(β(1)) содержит отрицательные элементы, то делаем вывод о неоптимальности плана, соответствующего базису β(1), и, выбрав наименьшую отрицательную оценку (-88), получаем номер столбца, вводимого в базис, l =4.
Переписываем столбец
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAACCAYAAABsfz2XAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAbSURBVBjTY2hsbGQgBUMIBob9QPyfAN4PUgsAZFQeoZBtxrEAAAAASUVORK5CYII=)
из таблицы
T1 в
Т2(1) и пересчитываем его координаты относительно текущего базиса, т. е. умножаем матрицу Δ
-1(β
(q)), расположенную в таблице
Т2(1) слева, на
а4.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAACCAYAAABsfz2XAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAAbSURBVBjTY2hsbGQgBUMIBob9QPyfAN4PUgsAZFQeoZBtxrEAAAAASUVORK5CYII=)
После заполнения таблицы
Т2(1) данными по вводимому в новый базис столбцу можно перейти к определению номера выводимого столбца. Эта процедура осуществляется в полной аналогии с обычным симплекс-методом. Рассмотрев отношения элементов
bi(β
(1)) и
ai,l(β
(1)) для {
iÎ1:
m| ai,l(β
(1))>0} и определив минимальное из них, находим, что
r =2. Следовательно, столбец с номером
N2(β
(q)) =2 должен быть выведен из базиса. Таким образом, получаем очередной допустимый базис задачи с
N(β
(2)) ={5, 4, 3}. Элемент
a2,3(β
(1)) является ведущим (обведен кружком). Применив формулы (1.43)-(1.46), переходим к симплекс-таблице, соответствующей второй итерации
Т2(2), и полагаем индекс текущей итерации
q = 2.