使用C++实现simplex算法

代码如下：

#include<iostream>
#include<cmath>
using namespace std;
#define M 10000
//全局变量
float kernel[11][31];//核心矩阵表
int m = 0, n = 0, t = 0;//m:结构向量的个数
//n:约束不等式个数
//t:目标函数类型：－1代表求求最小值，1代表求最大值
//输入接口函数
void input()
{
//读入所求问题的基本条件
cout << "－－－－－－－－－－参 数 输 入－－－－－－－－－－－" << endl;
cout << "请按提示输入下列参数：" << endl << endl;
cout << " 结构向量数m: " << " m= ";
cin >> m;
cout << endl << " 约束不等式数n:" << " n= ";
cin >> n;
int i, j;
//初始化核心向量
for (i = 0; i <= n + 1; i++)
for (j = 0; j <= m + n + n; j++)
kernel[i][j] = 0;
//读入约束条件
cout << endl << " 约束方程矩阵的系数及不等式方向（1代表<=,-1代表>=）:" << endl << endl << " ";
for (i = 1; i <= m; i++)
cout << " x" << i;
cout << " 不等式方向 " << " 常数项" << endl;
for (i = 1; i <= n; i++)
{
cout << " 不等式" << i << " ";
for (j = 1; j <= m + 2; j++)
cin >> kernel[i][j];
}

for (i = 1; i <= n; i++)
{
kernel[i][0] = kernel[i][m + 2];
kernel[i][m + 2] = 0;
}
//读入目标条件
cout << endl << endl << " 目标函数的系数及类型（求最小值:1；求最大值:-1）:" << endl << endl << " ";
for (i = 1; i <= m; i++)
cout << "x" << i << " ";
cout << "类型" << endl << " ";
cout << " 目标函数: ";
for (i = 1; i <= m; i++)
cin >> kernel[0][i];
cin >> t;
//矩阵调整
if (t == -1)
for (i = 1; i <= m; i++)
kernel[0][i] = (-1)*kernel[0][i];
for (i = 1; i <= n; i++)
{
kernel[i][m + i] = kernel[i][m + 1];
if (i != 1)
kernel[i][m + 1] = 0;
}
}

//算法函数
void comput()
{
int i, j, flag, temp1, temp2, h, k = 0, temp3[10];
float a, b[11], temp, temp4[11], temp5[11], f = 0, aa, d, c;
//初始化
for (i = 1; i <= n; i++)
temp3[i] = 0;
for (i = 0; i < 11; i++)
{
temp4[i] = 0;
temp5[i] = 0;
}
for (i = 1; i <= n; i++)
{
if (kernel[i][m + i] == -1)
{
kernel[i][m + n + i] = 1;
kernel[0][m + n + i] = M;
temp3[i] = m + n + i;
}
else
temp3[i] = m + i;
}
for (i = 1; i <= n; i++)
temp4[i] = kernel[0][temp3[i]];

//循环求解
do{
for (i = 1; i <= m + n + n; i++)
{
a = 0;
for (j = 1; j <= n; j++)
a += kernel[j][i] * temp4[j];
kernel[n + 1][i] = kernel[0][i] - a;
}
for (i = 1; i <= m + n + n; i++)
{
if (kernel[n + 1][i] >= 0) flag = 1;
else
{
flag = -1;
break;
}
}
if (flag == 1)
{
for (i = 1; i <= n; i++)
{
if (temp3[i] <= m + n) temp1 = 1;
else
{
temp1 = -1;
break;
}
}
//输出结果
cout << endl << endl;
cout << "－－－－－－－－－－结 果 输 出－－－－－－－－－－－" << endl << endl;
if (temp1 == 1)
{
cout << " 此线性规划的最优解存在!" << endl << endl << " 最优解为：" << endl << endl << " ";
for (i = 1; i <= n; i++)
temp5[temp3[i]] = kernel[i][0];
for (i = 1; i <= m; i++)
f += t*kernel[0][i] * temp5[i];

for (i = 1; i <= m; i++)
{
cout << "x" << i << " = " << temp5[i];
if (i != m)
cout << "， ";
}
cout << " ;" << endl << endl << " 最优目标函数值f= " << f << endl << endl;
return;
}
else
{
cout << " 此线性规划无解" << endl << endl;
return;
}
}
if (flag == -1)
{
temp = 100000;
for (i = 1; i <= m + n + n; i++)
if (kernel[n + 1][i] < temp)
{
temp = kernel[n + 1][i];
h = i;
}

for (i = 1; i <= n; i++)
{
if (kernel[i][h] <= 0) temp2 = 1;
else {
temp2 = -1;
break;

}
}
}
if (temp2 == 1)
{
cout << "此线性规划无约束";
return;
}
if (temp2 == -1)
{
c = 100000;
for (i = 1; i <= n; i++)
{
if (kernel[i][h] != 0) b[i] = kernel[i][0] / kernel[i][h];
if (kernel[i][h] == 0) b[i] = 100000;
if (b[i] < 0) b[i] = 100000;
if (b[i] < c)
{
c = b[i];
k = i;
}
}
temp3[k] = h;
temp4[k] = kernel[0][h];
d = kernel[k][h];
for (i = 0; i <= m + n + n; i++)
kernel[k][i] = kernel[k][i] / d;
for (i = 1; i <= n; i++)
{
if (i == k)
continue;
aa = kernel[i][h];
for (j = 0; j <= m + n + n; j++)
kernel[i][j] = kernel[i][j] - aa*kernel[k][j];
}
}
} while (1);
return;
}

int main()
{
cout << "-------------------单纯形算法程序----------------------" << endl << endl;
input();
comput();
system("pause");
return 1;
}