利用修正单纯形法解线性规划问题

1、利用修正单纯形法解线性规划问题软件示意：二 代码说明：Dim A(1 To 3, 1 To 6) As Double ' 矩阵 ADim a1(1 To 3) As Double Dim a2(1 To 3) As Double Dim a3(1 To 3) As DoubleDim a4(1 To 3) As Double Dim a5(1 To 3) As DoubleDim a6(1 To 3) As Double矩阵 A 的第一列向量 矩阵 A 的第二列向量 矩阵 A 的第三列向量 矩阵 A 的第四列向量 矩阵 A 的第五列向量 矩阵 A 的第六列向量Dim B_(1 To 3

2、, 1 To 3) As Double '基矩阵 B 的逆矩阵Dim XB(1 To 3) As Double ' 基本可行解Dim b(1 To 3) As Double ' 右端向量 bDim C(1 To 6) As Double 'Dim CB(1 To 3) As Double检验数基本可行解对应的检验数Dim (1 To 3) As Double ' 单纯形乘子矢量Dim r(1 To 6) As Double ' 检验矢量 rDim r_min As Double ' 检验矢量最小值Dim k_sign As Integer

3、 '检验矢量最小值对应的位置Dim Y(1 To 3, 0 To 6) As Double ' 矩阵 yDim just_vector(1 To 3) As DoubleDim liji_min As Double ' 用于判断离基变量所用值Dim r_sign As Integer ' 用于记录离基变量对应的位置Dim main_yuan As Double ' 用于存放主元Dim Erk(1 To 3, 1 To 3) As DoubleDim Exchange_B(1 To 3, 1 To 3) '在矩阵 Erk 与矩阵 B_进行乘法运算时

4、，作为矩阵 B_的替换矩阵Dim Exchange_XB(1 To 3) ' 在矩阵 Erk 与 XB_进行乘法运算时，作为 XB_的替 换矩阵Dim iterative_time As Integer ' 定义迭代的次数窗口 1开始了迭代循环Dim XB_optimization(1 To 6) As Double '最优解Private Sub Command1_Click()'For iterative_time = 1 To 1000 ' Select Case k_signCase 1If (r_sign - 3) = 3 ThenCB(1)

5、= C(2) ' 付值给基本可行解对应的检验数CB(2) = C(3)CB(3) = C(6)XB_optimization(1) = 0XB_optimization(2) = XB(1)XB_optimization(3) = XB(2)XB_optimization(4) = 0XB_optimization(5) = 0XB_optimization(6) = XB(3) End IfCase 2If (r_sign - 3) = 1 ThenCB(1) = C(2) ' 付值给基本可行解对应的检验数CB(2) = C(5)CB(3) = C(6)XB_optimiza

6、tion(1) = 0XB_optimization(2) = XB(1)XB_optimization(3) = 0XB_optimization(4) = 0XB_optimization(5) = XB(2)XB_optimization(6) = XB(3)End IfCase 3If (r_sign - 3) = 2 ThenCB(1) = C(2) ' 付值给基本可行解对应的检验数CB(2) = C(3)CB(3) = C(6)XB_optimization(1) = 0XB_optimization(2) = XB(1)XB_optimization(3) = XB(2)

7、XB_optimization(4) = 0XB_optimization(5) = 0XB_optimization(6) = XB(3)End IfEnd SelectFor i = 1 To 3 ' 计算单纯形乘子矢量(i) = CB(1) * B_(1, i) + CB(2) * B_(2, i) + CB(3) * B_(3, i) Next iFor j = 1 To 6 ' r(j) = C(j) - ( j)Next j计算检验矢量 r(1) * A(1, j) +(2) * A(2, j) +(3) * A(3,r_min = r(1) '预先给定一个

8、值k_sign = 1For i = 1 To 6 '找出最小检验值If (r(i) < r_min) Thenr_min = r(i) '最小检验值k_sign = i '最小检验值所在位置 , 对应进基矢量位置End IfNext iIf r_min < 0 ThenFor i = 1 To 3 'Y(i, k_sign)+ B_(i, 3) * A(3, k_sign) Next i对应进基矢量所得的 y 值= B_(i, 1) * A(1, k_sign) + B_(i, 2) * A(2, k_sign)For i = 1 To 3 

9、9; 确定离基变量If Y(i, k_sign) <> 0 Then just_vector(i) = Y(i, 0) / Y(i, k_sign)End IfNext iFor i = 1 To 3If (just_vector(i) > 0 Then liji_min = just_vector(i) ' Exit ForEnd IfNext i预先给定一个值r_sign = 4 For i = 1 To 3 ' 找出最小检验值If (just_vector(i) <= liji_min) And (just_vector(i) > 0)The

10、nliji_min = just_vector(i) r_sign = i + 3 'End IfNext i最小检验值最小检验值所在位置 , 对应进基矢量位置main_yuan = Y(r_sign - 3, k_sign) If main_yuan <> 0 ThenSelect Case (r_sign - 3) '计算矩阵 ErkCase 1Erk(1, 1) = 1 / main_yuanErk(2, 1) = -Y(2, k_sign) / main_yuanErk(3, 1) = -Y(3, k_sign) / main_yuan For i = 2

11、To 3For j = 1 To 3 Erk(j, i) = A(j, i + 3)Next jNext iCase 2Erk(1, 2) = -Y(1, k_sign) / main_yuanErk(2, 2) = 1 / main_yuanErk(3, 2) = -Y(3, k_sign) / main_yuan For j = 1 To 3Erk(j, 1) = A(j, 4) Next j For j = 1 To 3Erk(j, 3) = A(j, 6) Next jCase 3Erk(1, 3) = -Y(1, k_sign) / main_yuanErk(2, 3) = -Y(2

12、, k_sign) / main_yuanErk(3, 3) = 1 / main_yuanFor i = 1 To 2For j = 1 To 3 Erk(j, i) = A(j, i + 4)Next jNext iEnd SelectEnd IfFor i = 1 To 3 '给矩阵 Exchange_B(i, j) 付值For j = 1 To 3Exchange_B(i, j) = B_(i, j)Next jNext iFor i = 1 To 3 '计算 B 的新可逆矩阵 B_For j = 1 To 3B_(i, j) = Erk(i, 1) * Exchang

13、e_B(1, j) + Erk(i, 2) Exchange_B(2, j) + Erk(i, 3) * Exchange_B(3, j)Next jNext iFor i = 1 To 3 '给 Exchange_XB(i) 付值Exchange_XB(i) = XB(i)Next iFor i = 1 To 3 ' 计算基本可行解XB(i) = Erk(i, 1) * Exchange_XB(1) + Erk(i, 2) Exchange_XB(2) + Erk(i, 3) * Exchange_XB(3)Y(i, 0) = XB(i)Next iElseMsgBox (&

14、quot; 优化完毕 !")Exit ForEnd IfNext iterative_timeCommand2.Enabled = True ' 使能按钮Command3.Enabled = True ' 使能按钮Form1.Text1(1).Text =XB_optimization(1) '显示最优解x1Form1.Text1(2).Text =XB_optimization(2) '显示最优解x2Form1.Text1(3).Text =XB_optimization(3) '显示最优解x3Form1.Text1(4).Text =XB_

15、optimization(4) '显示最优解x4Form1.Text1(5).Text =XB_optimization(5) '显示最优解x5Form1.Text1(6).Text =XB_optimization(6) '显示最优解x6Form1.Text1(0).Text= C(1) *XB_optimization(1)+C(2) *XB_optimization(2)+ C(3) *XB_optimization(3)+C(4) *XB_optimization(4)+ C(5) *XB_optimization(5)+C(6) *XB_optimizatio

16、n(6) '显示最优值 ZForm1.Text1(7) = iterative_time - 1 '显示迭代次数End SubPrivate Sub Command2_Click()End ' 结束程序End SubPrivate Sub Command3_Click()Form1.Show ' 调用优化结果显示窗口 End SubPrivate Sub Form_Load()Dim i, j As IntegerFor i = 1 To 3 '付值给系数矩阵 A付值给系数矩阵 AFor j = 1 To 6A(i, j) = Quotiety_A(j

17、+ 6 * (i - 1).Text 'Next jNext iFor i = 1 To 6 '将矩阵 A 列分块( a1,a2,a3,a4,a5,a6For j = 1 To 3 Select Case iCase 1 a1(j) = A(j, i)Case 2 a2(j) = A(j, i)Case 3 a3(j) = A(j, i)Case 4 a4(j) = A(j, i)Case 5 a5(j) = A(j, i)Case 6 a6(j) = A(j, i)End SelectNext jNext iFor i = 1 To 3 ' 付值给基矩阵 B的逆矩阵

18、B_For j = 1 To 3 Select Case iCase 1 B_(j, i) = a4(j)Case 2 B_(j, i) = a5(j)Case 3 B_(j, i) = a6(j)End SelectNext jNext iFor i = 1 To 6 '付值给检验数Select Case iCase 1C(1) = C_quotiety(0).TextCase 2C(2) = C_quotiety(1).TextCase 3C(3) = C_quotiety(2).TextCase 4C(4) = C_quotiety(3).TextCase 5C(5) = C_quotiety(4).TextCase 6C(6) = C_quotiety(5).TextEnd Select付值给右端向量 bNext i b(1) = b_quotiety(0).Textb(2)