单纯形算法（Simplex Method）

 

#include<iostream>
#define N1 4
#define N2 6
#define INF -100000
#define MAX 100000
using namespace std;
//约束条件系数
double a[N1][N2] = {{0},{0,1,-2,1,0,0},
                        {0,0,1,-3,1,0},
                        {0,0,1,-1,0,1}};
double b[N1] = {0,2,1,2}; // 向量b

double e[N2] = {0,0,1,-2,0,0};//检验数向量
double RHS = 0;//目标函数值
int x[N1] = {0,0,0,0}; // 存放基本可行解
// 找出初值解
void BeginOne()
{
    //进行列搜索， 得到初始解
    bool y[N2] = {0};
    //int num = 1;
    int index = 0;
    for(int j=1; j<N2; ++j){
      int cnt = 0;
     for(int i=1; i<N1; ++i)
      if(a[i][j]){
         ++cnt;
         index = i;
       }
      if(cnt==1&&y[j]==0){
        x[index] = j;
        y[j] = 1;
      }
    }
    cout<<"得到初始基本可行解为:"<<endl;
    for(int i=1; i<N1; ++i)
        cout<<"x("<<x[i]<<")"<<" = "<<b[i]/a[i][x[i]]<<endl;
}
void GetFirstForm()
{
     double tmp = 0;
     for(int j=1; j<N1; ++j)
         if(e[x[j]]!=0){
         for(int i=1; i<N2; ++i){
              tmp = e[x[j]];
             e[i] -=   tmp*a[j][i];
            }
         RHS -= tmp*b[j];
     }
}
int CheckVector()
{
    bool IsNegative = 1;
    bool IsEnd = 1;
    for(int i=1; i<N2; ++i)
       if(e[i]>0){
         IsNegative = 0;
         for(int j=1; j<N1; ++j)
           if(a[j][i]>0)
             IsEnd = 0;
         if(IsEnd){
           cout<<"此LP问题无界!"<<endl;
           return 0;
         }
       }
   if(IsNegative){
      cout<<"迭代得到一个最优解:RHS = "<<RHS<<endl;
      for(int i=1; i<N1; ++i)
        cout<<"x("<<x[i]<<")"<<" = "<<b[i]/a[i][x[i]]<<endl;
       return 0;
   }
   return 1;
}
int MaxEj()
{
    double max = INF;
    int index = 0;
    for(int i=1; i<N2; ++i)
      if(max<e[i]){
        max = e[i];
        index = i;
      }
      return index;
}
int main()
{
    BeginOne();
    //得到第一张单纯行表
    GetFirstForm();
    cout<<"The First Form Of Simplex Method:"<<endl;
    cout<<"Vec  ";
    for(int i=1; i<N2; ++i)
      cout<<e[i]<<" ";
      cout<<RHS<<endl;
    for(int i=1; i<N1; ++i){
      cout<<"x("<<x[i]<<") ";
      for(int j=1; j<N2; ++j)
        cout<<a[i][j]<<" ";
      cout<<b[i]<<endl;
    }
    /*循环得出最优解*/
    while(CheckVector()){
      int ej = MaxEj();
      double min = MAX;
      int Xiout = 0;
      //找到最小的b(i)/a(i)(ej)
      for(int i=1; i<N1; ++i)
        if(a[i][ej]>0&&min>b[i]/a[i][ej]){
           min = b[i]/a[i][ej];
           Xiout = i;
        }
        x[Xiout] = ej;
        for(int i=1; i<N2; ++i)
          if(ej!=i){ /*ej=Xiout Error Failed*/
           a[Xiout][i] = a[Xiout][i]/a[Xiout][ej];
           }
        /*Error will be found*/
        b[Xiout]/=a[Xiout][ej];
        a[Xiout][ej] = 1;
        //化检验数向量
        double tmp = e[ej];
        for(int i=1; i<N2; ++i)
           e[i] -= tmp*a[Xiout][i];
        RHS -= tmp*b[Xiout];
        for(int i=1; i<N1; ++i){
          if(i!=Xiout){
           tmp = a[i][ej];
          for(int j=1; j<N2; ++j)
            a[i][j] -= tmp*a[Xiout][j];
          b[i] -= tmp*b[Xiout];
          }
        }
    }
    system("pause");
    return 0;
}