线性规划VB求解

线性规划VB求解

Rem 定义动态数组
Dim a() As Single, c() As Single, b() As Single, cb() As Single
Dim aa() As Single, cba() As Single, xcb() As Integer, xb() As Integer
Dim m As Integer, n As Integer, l As Integer, k As Integer, cc As Integer, cm As Integer, ka As Integer
Dim qq As Single, tt As Single, z As Single

Private Sub Command1_Click()

Show
n = Val(InputBox("请输入线性规划典范型方程变量的个数 N=?", "输入数据", 0))
m = Val(InputBox("请输入线性规划典范型方程约束条件的个数 M=?", "输入数据", 0))

Rem 给数组分配空间
ReDim a(0 To m + 1, 0 To n + 2)
ReDim aa(1 To m + 1, 1 To n + 2)
ReDim c(n)
ReDim b(m)
ReDim cb(m)
ReDim cba(n)
ReDim xcb(n)
ReDim xb(m)


Rem 对线性规划约束方程增广矩阵A（）进行归零计算
For i = 0 To m + 1
    For j = 0 To n + 2
      a(i, j) = 0
    Next j
Next i

Rem 输入线性规划约束方程系数矩阵A（）
For i = 1 To m
  For j = 1 To n
    a(i, j) = Val(InputBox("请输入典范型方程约束条件矩阵的系数 a(" & Str(i) & "," & Str(j) & ")：", "输入数据", 0))
  Next j
Next i

Rem 输入线性规划约束方程右端常数B（）
For i = 1 To m
  b(i) = Val(InputBox("请输入典范型方程约束条件右端的常数 b(" & Str(i) & ")：", "输入数据", 0))
Next i

Rem 把右端常数写入增广矩阵A（）中
For i = 1 To m
  a(i, n + 1) = b(i)
Next i

Rem 输入线性规划目标函数的系数C（）
For i = 1 To n
  c(i) = Val(InputBox("请输入典范型方程目标函数的系数 c(" & Str(i) & ")：", "输入数据", 0))
Next i

Rem 把目标函数的系数写入增广矩阵A（）中
For i = 1 To n
  a(0, i) = c(i)
Next i

Rem 输入线性规划单纯形初始表中基变量在目标函数中的系数CB（）
For i = 1 To m
  cb(i) = Val(InputBox("请输入线性规划单纯形初始表中基变量在目标函数中的系数CB（" & Str(i) & ")：", "输入数据", 0))
Next i

Rem 把基变量目标函数的系数写入增广矩阵A（）中
For i = 1 To m
  a(i, 0) = cb(i)
Next i

Rem 记录基变量下标值
For i = 1 To m
   xb(i) = Val(InputBox("请输入典范型方程第" & Str(i) & "行，基变量的下标：", "输入数据", 0))
Next i

Rem 检验数的累积数归零并计算检验数
For i = 1 To n
  cba(i) = 0
Next i
For i = 1 To n
  For j = 1 To m
    cba(i) = cba(i) + a(j, 0) * a(j, i)
  Next j
  a(m + 1, i) = a(0, i) - cba(i)
Next i

Rem 计算目标函数值
z = 0
For i = 1 To m
  z = z + a(i, 0) * a(i, n + 1)
Next i
a(m + 1, n + 1) = z

Rem 打印增广矩阵A（）
For i = 0 To m + 1
  For j = 0 To n + 2
    Print a(i, j);
  Next j
  Print
Next i
Print


Rem 判断所有检验数是否都小于等于零
cc = 0
For i = 1 To n
   If a(m + 1, i) <= 0 Then
      cc = cc + 1
   End If
Next i

Rem 统计检验数为零的个数
cm = 0
For i = 1 To n
  If a(m + 1, i) = 0 Then
     cm = cm + 1
  End If
Next i

Print "cc="; cc, "cm="; cm


Rem 判断此单纯形表是否为最优单纯形表
Do While cc < n
   
   Rem 统计检验数最大值并确定进基列
   qq = 0.00001
   l = 0
   For i = 1 To n
     If a(m + 1, i) > qq Then
        qq = a(m + 1, i)
        l = i
     End If
   Next i
   Print
   Print "l="; l,

   Rem 统计进基列上A（i,j）小于等于零的个数
   ka = 0
   For i = 1 To m
     If a(i, l) <= 0 Then
        ka = ka + 1
     End If
   Next i
   
   Rem 若各进基列上A（i,j）全都小于等于零，则本线性规划有无界解
   If ka = m Then
      Print "本线性规划有无界解！"
      Print
      Exit Do
   End If
   
   Rem  计算比值θ并按最小比值准则确定出基行
   For i = 1 To m
      If a(i, l) > 0 Then
         a(i, n + 2) = a(i, n + 1) / a(i, l)
      End If
   Next i
   
   tt = 10000
   k = 0
   For i = 1 To m
     If a(i, l) > 0 And a(i, n + 2) < tt Then
        tt = a(i, n + 2)
        k = i
     End If
   Next i
   
   Print "k="; k
   Print
      
     
   Rem 进行初等行变换时，对临时数组归零计算
   For i = 1 To m + 1
     For j = 1 To n + 2
         aa(i, j) = 0
     Next j
   Next i
   
   Rem 确定枢轴元素，进行初等行变换
   oo = a(k, l)
   For i = 1 To n + 1
      aa(k, i) = a(k, i) / oo
   Next i
   
      
   For i = 1 To m
      If i <> k Then
        For j = 1 To n + 1
          aa(i, j) = a(i, j) + a(k, j) * (-a(i, l))
       
        Next j
      End If
          
   Next i
     
   Rem 把临时数组AA（）的数据写到增广矩阵A（）中去
   For i = 1 To m + 1
     For j = 1 To n + 2
        a(i, j) = aa(i, j)
     Next j
   Next i
      
   a(k, 0) = a(0, l)
   xb(k) = l
             
   Rem 检验数的累积数归零并计算检验数
   For i = 1 To n
     cba(i) = 0
   Next i
   For i = 1 To n
     For j = 1 To m
       cba(i) = cba(i) + a(j, 0) * a(j, i)
     Next j
     a(m + 1, i) = a(0, i) - cba(i)
   Next i

   Rem 计算目标函数值
   z = 0
   For i = 1 To m
      z = z + a(i, 0) * a(i, n + 1)
   Next i
   a(m + 1, n + 1) = z
   
   Rem 判断所有检验数是否都小于等于零
   cc = 0
   For i = 1 To n
     If a(m + 1, i) <= 0 Then
       cc = cc + 1
     End If
   Next i
    
   Rem 统计检验数为零的个数
   cm = 0
   For i = 1 To n
     If a(m + 1, i) = 0 Then
        cm = cm + 1
     End If
   Next i
  
    Rem 打印增广矩阵A（）
For i = 0 To m + 1
   For j = 0 To n + 2
    
     Print a(i, j);
   
   Next j
   Print
Next i
Print


Loop

Rem 判断此单纯形表是否为最优单纯形表
If cc = n Then
  
  Rem 判断本线性规划有唯一最优解或者有多重最优解
  If cm = m Then
      Print "本线性规划有唯一最优解！"
      Print "线性规划的最优解为："
  ElseIf cm > m Then
      Print "本线性规划有多重最优解！"
      Print "线性规划的最优值为："
  End If
End If
  
Rem 打印线性规划的解和目标函数值
For i = 1 To m
   
  Print "X(" & Str(xb(i)) & ")="; a(i, n + 1),
   
Next i
Print "其它变量为零。"
Print "Z="; a(m + 1, n + 1)
Print
  
Rem 打印增广矩阵A（）
For i = 0 To m + 1
   For j = 0 To n + 2
    
     Print a(i, j);
   
   Next j
   Print
Next i


End Sub