PSO优化算法求解TSP问题的C++实现
1、输入数据文件：bayg29.tsp
29个城市的编号和坐标数据如下所示；
1 1150.0 1760.0
2 630.0 1660.0
3 40.0 2090.0
4 750.0 1100.0
5 750.0 2030.0
6 1030.0 2070.0
7 1650.0 650.0
8 1490.0 1630.0
9 790.0 2260.0
10 710.0 1310.0
11 840.0 550.0
12 1170.0 2300.0
13 970.0 1340.0
14 510.0 700.0
15 750.0 900.0
16 1280.0 1200.0
17 230.0 590.0
18 460.0 860.0
19 1040.0 950.0
20 590.0 1390.0
21 830.0 1770.0
22 490.0 500.0
23 1840.0 1240.0
24 1260.0 1500.0
25 1280.0 790.0
26 490.0 2130.0
27 1460.0 1420.0
28 1260.0 1910.0
29 360.0 1980.0
2、头文件
#include <iostream>
#include <string>
#include <fstream>
#include <time.h>
#include <random>
using namespace std;
3、所需的类
代码中用到了四个类：City、Graph、Particle和PSO。
3.1 城市类City:
class City
{
public:
string name;//城市名称
double x, y;//城市点的二维坐标
void shuchu()
{
std::cout << name + ":" << "(" << x << "," << y << ")" << endl;
}
};
3.2 包含城市的地图类Graph：
class Graph
{
public:
City city[citycount];//城市数组
double distance[citycount][citycount];//城市间的距离矩阵
void Readcoordinatetxt(string txtfilename)//读取城市坐标文件的函数
{
ifstream myfile(txtfilename, ios::in);
double x = 0, y = 0;
int z = 0;
if (!myfile.fail())
{
int i = 0;
while (!myfile.eof() && (myfile >> z >> x >> y))
{
city[i].name = to_string(_Longlong(z));//城市名称转化为字符串
city[i].x = x; city[i].y = y;
i++;
}
}
else
cout << "文件不存在";
myfile.close();//计算城市距离矩阵
for (int i = 0; i < citycount; i++)
for (int j = 0; j < citycount; j++)
{
distance[i][j] = sqrt((pow((city[i].x - city[j].x), 2) + pow((city[i].y - city[j].y), 2)) / 10.0);//计算城市ij之间的伪欧式距离
if (round(distance[i][j] < distance[i][j]))distance[i][j] = round(distance[i][j]) + 1;
else distance[i][j] = round(distance[i][j]);
}
}
void shuchu()
{
cout << "城市名称 " << "坐标x" << " " << "坐标y" << endl;
for (int i = 0; i < citycount; i++)
city[i].shuchu();
cout << "距离矩阵： " << endl;
for (int i = 0; i < citycount; i++)
{
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
std::cout << distance[i][j] << endl;
else
std::cout << distance[i][j] << " ";
}
}
}
};
3.3 粒子类Particle:
class Particle
{
public:
int *x;//粒子的位置
int *v;//粒子的速度
double fitness;
void Init()
{
x = new int[citycount];
v = new int[citycount];
int *M = Random_N(citycount);
for (int i = 0; i < citycount; i++)
x[i] = *(M + i);
fitness = Evaluate(x);
for (int i = 0; i < citycount; i++)
{
v[i] = (int)distribution1(random);
}
}
void shuchu()
{
for (int i = 0; i < citycount; i++)
{
if (i == citycount - 1)
std::cout << x[i] <<") = "<<fitness<< endl;
else if(i==0)
std::cout <<"f("<< x[i] << ",";
else
std::cout << x[i] << ",";
}
}
};
3.4 粒子群优化算法类PSO：
class PSO
{
public:
Particle *oldparticle;
Particle *pbest, gbest;
double c1, c2,w;
int Itetime;
int popsize;
void Init(int Pop_Size,int itetime,double C1,double C2,double W)
{
Itetime = itetime;
c1 = C1;
c2 = C2;
w = W;
popsize = Pop_Size;
oldparticle = new Particle[popsize];
pbest = new Particle[popsize];
for (int i = 0; i < popsize; i++)
{
oldparticle[i].Init();
pbest[i].Init();
for (int j = 0; j < citycount; j++)
{
pbest[i].x[j] = oldparticle[i].x[j];
pbest[i].fitness = oldparticle[i].fitness;
}
}
gbest.Init(); gbest.fitness = INFINITY;//为全局最优粒子初始化
for (int i = 0; i < popsize; i++)
{
if (pbest[i].fitness < gbest.fitness)
{
gbest.fitness = pbest[i].fitness;
for (int j = 0; j < citycount; j++)
gbest.x[j] = pbest[i].x[j];
}
}
}
void Shuchu()
{
for (int i = 0; i < popsize; i++)
{
std::cout << "粒子" << i + 1<<"->";
oldparticle[i].shuchu();
}
}
void PSO_TSP(int Pop_size,int itetime, double C1, double C2, double W,double Vlimitabs,string filename)
{
Map_City.Readcoordinatetxt(filename);
Map_City.shuchu();
vmax = Vlimitabs; vmin = -Vlimitabs;
Init(Pop_size,itetime,C1,C2,W);
std::cout << "初始化后的种群如下：" << endl;
Shuchu();
ofstream outfile;
outfile.open("result.txt", ios::trunc);
outfile << "城市名称 " << "坐标x" << " " << "坐标y" << endl;
for (int i = 0; i < citycount; i++)
outfile << Map_City.city[i].name << " " << Map_City.city[i].x << " " << Map_City.city[i].y << endl;
outfile << "距离矩阵： " << endl;
for (int i = 0; i < citycount; i++)
{
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
outfile << Map_City.distance[i][j] << endl;
else
outfile << Map_City.distance[i][j] << " ";
}
}
outfile << "初始化后的种群如下：" << endl;
for (int i = 0; i < popsize; i++)
{
outfile << "粒子" << i + 1 << "->";
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
outfile << oldparticle[i].x[j] << ") = " << oldparticle[i].fitness << endl;
else if (j == 0)
outfile << "f(" << oldparticle[i].x[j] << ",";
else
outfile << oldparticle[i].x[j] << ",";
}
}
for (int ite = 0; ite < Itetime; ite++)
{
for (int i = 0; i < popsize; i++)
{
//更新粒子速度和位置
for (int j = 0; j < citycount; j++)
{
oldparticle[i].v[j] = (int)(w*oldparticle[i].v[j] + c1*distribution(random)*(pbest[i].x[j] - oldparticle[i].x[j]) + c2*distribution(random)*(gbest.x[j] - oldparticle[i].x[j]));
if (oldparticle[i].v[j] > vmax)//粒子速度越界调整
oldparticle[i].v[j] = (int)vmax;
else if (oldparticle[i].v[j] < vmin)
oldparticle[i].v[j] = (int)vmin;
oldparticle[i].x[j] += oldparticle[i].v[j];
if (oldparticle[i].x[j] > citycount)oldparticle[i].x[j] = citycount;//粒子位置越界调整
else if (oldparticle[i].x[j] < 1) oldparticle[i].x[j] = 1;
}
//粒子位置有效性调整，必须满足解空间的条件
Adjuxt_validParticle(oldparticle[i]);
oldparticle[i].fitness = Evaluate(oldparticle[i].x);
pbest[i].fitness = Evaluate(pbest[i].x);
if (oldparticle[i].fitness < pbest[i].fitness)
{
for (int j = 0; j < citycount; j++)
pbest[i].x[j] = oldparticle[i].x[j];
}//更新单个粒子的历史极值
for (int j = 0; j < citycount; j++)
gbest.x[j] = pbest[i].x[j];//更新全局极值
for (int k = 0; k < popsize && k!=i; k++)
{
if (Evaluate(pbest[k].x) < Evaluate(gbest.x))
{
for (int j = 0; j < citycount; j++)
gbest.x[j] = pbest[k].x[j];
gbest.fitness = Evaluate(gbest.x);
}
}
}
outfile << "第"<<ite+1<<"次迭代后的种群如下：" << endl;
for (int i = 0; i < popsize; i++)
{
outfile << "粒子" << i + 1 << "->";
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
outfile << oldparticle[i].x[j] << ") = " << oldparticle[i].fitness << endl;
else if (j == 0)
outfile << "f(" << oldparticle[i].x[j] << ",";
else
outfile << oldparticle[i].x[j] << ",";
}
}
std::cout << "第" <<ite+1<< "次迭代后的最好粒子：";
outfile << "第" << ite + 1 << "次迭代后的最好粒子："<<endl;
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
outfile << gbest.x[j] << ") = " << gbest.fitness << endl;
else if (j == 0)
outfile << "f(" << gbest.x[j] << ",";
else
outfile << gbest.x[j] << ",";
}
gbest.shuchu();
}
outfile.close();
}
};
4、自定义函数
4.1 随机生成1~n的一个排列的函数
int * Random_N(int n)
{
int *geti;
geti = new int[n];
int j = 0;
while (j<n)
{
while (true)
{
int flag = -1;
int temp = rand() % n + 1;
if (j > 0)
{
int k = 0;
for (; k < j; k++)
{
if (temp == *(geti + k))break;
}
if (k == j)
{
*(geti + j) = temp;
flag = 1;
}
}
else
{
*(geti + j) = temp;
flag = 1;
}
if (flag == 1)break;
}
j++;
}
return geti;
}
4.2 粒子适应值计算函数
double Evaluate(int *x)//计算粒子适应值的函数
{
double fitnessvalue = 0;
for (int i = 0; i < citycount - 1; i++)
fitnessvalue += Map_City.distance[x[i] - 1][x[i + 1] - 1];
fitnessvalue += Map_City.distance[x[citycount - 1] - 1][x[0] - 1];
return fitnessvalue;
}
4.3 粒子路径有效性调整函数
void Adjuxt_validParticle(Particle p)//调整粒子有效性的函数，使得粒子的位置符合TSP问题解的一个排列
{
int route[citycount];//1-citycount
bool flag[citycount];//对应route数组中是否在粒子的位置中存在的数组，参考数组为route
int biaoji[citycount];//对粒子每个元素进行标记的数组,参考数组为粒子位置x
for (int j = 0; j < citycount; j++)
{
route[j] = j + 1;
flag[j] = false;
biaoji[j] = 0;
}
//首先判断粒子p的位置中是否有某个城市且唯一，若有且唯一，则对应flag的值为true,
for (int j = 0; j < citycount; j++)
{
int num = 0;
for (int k = 0; k < citycount; k++)
{
if (p.x[k] == route[j])
{
biaoji[k] = 1;//说明粒子中的k号元素对应的城市在route中，并且是第一次出现才进行标记
num++; break;
}
}
if (num == 0) flag[j] = false;//粒子路线中没有route[j]这个城市
else if (num == 1) flag[j] = true;//粒子路线中有route[j]这个城市
}
for (int k = 0; k < citycount; k++)
{
if (flag[k] == false)//粒子路线中没有route[k]这个城市，需要将这个城市加入到粒子路线中
{
int i = 0;
for (; i < citycount; i++)
{
if (biaoji[i] != 1)break;
}
p.x[i] = route[k];//对于标记为0的进行替换
biaoji[i] = 1;
}
}
}
5、全局变量
const int citycount = 29;
double vmax = 1, vmin = -1;
std::default_random_engine random(time(NULL));
static std::uniform_real_distribution<double> distribution(0.0, std::nextafter(1.0, DBL_MAX));// C++11提供的实数均匀分布模板类
static std::uniform_real_distribution<double> distribution1(vmin, std::nextafter(vmax, DBL_MAX));
Graph Map_City;//定义全局对象图,放在Graph类后
PSO pso;//定义粒子群优化算法类的对象，放在PSO类后
6、主函数
main.()函数
int main()
{
system("mode con cols=200");//改变宽高
system("color fc");//改变颜色
std::cout << "粒子群优化算法求解TSP旅行商问题" << endl;
pso.PSO_TSP(30,500,2,2,0.8,3.0, "E:\\计算智能代码\\PSO_TSP\\PSO_TSP\\bayg29.tsp");
system("pause");
return 0;
}
7、运行结果
7.1 控制台运行结果：
7.2 生成的result.txt文件结果：
8 Matlab绘制最优路径结果
8.1 Matlab导入数据
8.2 编写tspplot.m脚本文件
index=[21,12,6,9,3,5,1,2,4,10,13,8,16,7,11,19,15,14,18,17,22,20,25,23,27,24,28,26,29];
index=index';
myindex=sort(index);
X=x;
Y=y;
for i=1:29
X(i)=x(index(i))
Y(i)=y(index(i))
end
figure;
subplot(121);
scatter(x,y,'r.');
for i=1:29
tx=num2str(i);
text(x(i)+1,y(i)+1,tx);
end
subplot(122);
plot(X,Y,'-');
for i=1:29
tx=num2str(index(i));
text(X(i)+1,Y(i)+1,tx);
end
8.3 脚本运行结果
附录（完整代码）
#include <iostream>
#include <string>
#include <fstream>
#include <time.h>
#include <random>
using namespace std;
const int citycount = 29;
double vmax = 1, vmin = -1;
std::default_random_engine random(time(NULL));
static std::uniform_real_distribution<double> distribution(0.0, std::nextafter(1.0, DBL_MAX));// C++11提供的实数均匀分布模板类
static std::uniform_real_distribution<double> distribution1(vmin, std::nextafter(vmax, DBL_MAX));
class City
{
public:
string name;//城市名称
double x, y;//城市点的二维坐标
void shuchu()
{
std::cout << name + ":" << "(" << x << "," << y << ")" << endl;
}
};
class Graph
{
public:
City city[citycount];//城市数组
double distance[citycount][citycount];//城市间的距离矩阵
void Readcoordinatetxt(string txtfilename)//读取城市坐标文件的函数
{
ifstream myfile(txtfilename, ios::in);
double x = 0, y = 0;
int z = 0;
if (!myfile.fail())
{
int i = 0;
while (!myfile.eof() && (myfile >> z >> x >> y))
{
city[i].name = to_string(_Longlong(z));//城市名称转化为字符串
city[i].x = x; city[i].y = y;
i++;
}
}
else
cout << "文件不存在";
myfile.close();//计算城市距离矩阵
for (int i = 0; i < citycount; i++)
for (int j = 0; j < citycount; j++)
{
distance[i][j] = sqrt((pow((city[i].x - city[j].x), 2) + pow((city[i].y - city[j].y), 2)) / 10.0);//计算城市ij之间的伪欧式距离
if (round(distance[i][j] < distance[i][j]))distance[i][j] = round(distance[i][j]) + 1;
else distance[i][j] = round(distance[i][j]);
}
}
void shuchu()
{
cout << "城市名称 " << "坐标x" << " " << "坐标y" << endl;
for (int i = 0; i < citycount; i++)
city[i].shuchu();
cout << "距离矩阵： " << endl;
for (int i = 0; i < citycount; i++)
{
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
std::cout << distance[i][j] << endl;
else
std::cout << distance[i][j] << " ";
}
}
}
};
Graph Map_City;//定义全局对象图,放在Graph类后
int * Random_N(int n)
{
int *geti;
geti = new int[n];
int j = 0;
while (j<n)
{
while (true)
{
int flag = -1;
int temp = rand() % n + 1;
if (j > 0)
{
int k = 0;
for (; k < j; k++)
{
if (temp == *(geti + k))break;
}
if (k == j)
{
*(geti + j) = temp;
flag = 1;
}
}
else
{
*(geti + j) = temp;
flag = 1;
}
if (flag == 1)break;
}
j++;
}
return geti;
}
double Evaluate(int *x)//计算粒子适应值的函数
{
double fitnessvalue = 0;
for (int i = 0; i < citycount - 1; i++)
fitnessvalue += Map_City.distance[x[i] - 1][x[i + 1] - 1];
fitnessvalue += Map_City.distance[x[citycount - 1] - 1][x[0] - 1];
return fitnessvalue;
}
class Particle
{
public:
int *x;//粒子的位置
int *v;//粒子的速度
double fitness;
void Init()
{
x = new int[citycount];
v = new int[citycount];
int *M = Random_N(citycount);
for (int i = 0; i < citycount; i++)
x[i] = *(M + i);
fitness = Evaluate(x);
for (int i = 0; i < citycount; i++)
{
v[i] = (int)distribution1(random);
}
}
void shuchu()
{
for (int i = 0; i < citycount; i++)
{
if (i == citycount - 1)
std::cout << x[i] <<") = "<<fitness<< endl;
else if(i==0)
std::cout <<"f("<< x[i] << ",";
else
std::cout << x[i] << ",";
}
}
};
void Adjuxt_validParticle(Particle p)//调整粒子有效性的函数，使得粒子的位置符合TSP问题解的一个排列
{
int route[citycount];//1-citycount
bool flag[citycount];//对应route数组中是否在粒子的位置中存在的数组，参考数组为route
int biaoji[citycount];//对粒子每个元素进行标记的数组,参考数组为粒子位置x
for (int j = 0; j < citycount; j++)
{
route[j] = j + 1;
flag[j] = false;
biaoji[j] = 0;
}
//首先判断粒子p的位置中是否有某个城市且唯一，若有且唯一，则对应flag的值为true,
for (int j = 0; j < citycount; j++)
{
int num = 0;
for (int k = 0; k < citycount; k++)
{
if (p.x[k] == route[j])
{
biaoji[k] = 1;//说明粒子中的k号元素对应的城市在route中，并且是第一次出现才进行标记
num++; break;
}
}
if (num == 0) flag[j] = false;//粒子路线中没有route[j]这个城市
else if (num == 1) flag[j] = true;//粒子路线中有route[j]这个城市
}
for (int k = 0; k < citycount; k++)
{
if (flag[k] == false)//粒子路线中没有route[k]这个城市，需要将这个城市加入到粒子路线中
{
int i = 0;
for (; i < citycount; i++)
{
if (biaoji[i] != 1)break;
}
p.x[i] = route[k];//对于标记为0的进行替换
biaoji[i] = 1;
}
}
}
class PSO
{
public:
Particle *oldparticle;
Particle *pbest, gbest;
double c1, c2,w;
int Itetime;
int popsize;
void Init(int Pop_Size,int itetime,double C1,double C2,double W)
{
Itetime = itetime;
c1 = C1;
c2 = C2;
w = W;
popsize = Pop_Size;
oldparticle = new Particle[popsize];
pbest = new Particle[popsize];
for (int i = 0; i < popsize; i++)
{
oldparticle[i].Init();
pbest[i].Init();
for (int j = 0; j < citycount; j++)
{
pbest[i].x[j] = oldparticle[i].x[j];
pbest[i].fitness = oldparticle[i].fitness;
}
}
gbest.Init(); gbest.fitness = INFINITY;//为全局最优粒子初始化
for (int i = 0; i < popsize; i++)
{
if (pbest[i].fitness < gbest.fitness)
{
gbest.fitness = pbest[i].fitness;
for (int j = 0; j < citycount; j++)
gbest.x[j] = pbest[i].x[j];
}
}
}
void Shuchu()
{
for (int i = 0; i < popsize; i++)
{
std::cout << "粒子" << i + 1<<"->";
oldparticle[i].shuchu();
}
}
void PSO_TSP(int Pop_size,int itetime, double C1, double C2, double W,double Vlimitabs,string filename)
{
Map_City.Readcoordinatetxt(filename);
Map_City.shuchu();
vmax = Vlimitabs; vmin = -Vlimitabs;
Init(Pop_size,itetime,C1,C2,W);
std::cout << "初始化后的种群如下：" << endl;
Shuchu();
ofstream outfile;
outfile.open("result.txt", ios::trunc);
outfile << "城市名称 " << "坐标x" << " " << "坐标y" << endl;
for (int i = 0; i < citycount; i++)
outfile << Map_City.city[i].name << " " << Map_City.city[i].x << " " << Map_City.city[i].y << endl;
outfile << "距离矩阵： " << endl;
for (int i = 0; i < citycount; i++)
{
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
outfile << Map_City.distance[i][j] << endl;
else
outfile << Map_City.distance[i][j] << " ";
}
}
outfile << "初始化后的种群如下：" << endl;
for (int i = 0; i < popsize; i++)
{
outfile << "粒子" << i + 1 << "->";
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
outfile << oldparticle[i].x[j] << ") = " << oldparticle[i].fitness << endl;
else if (j == 0)
outfile << "f(" << oldparticle[i].x[j] << ",";
else
outfile << oldparticle[i].x[j] << ",";
}
}
for (int ite = 0; ite < Itetime; ite++)
{
for (int i = 0; i < popsize; i++)
{
//更新粒子速度和位置
for (int j = 0; j < citycount; j++)
{
oldparticle[i].v[j] = (int)(w*oldparticle[i].v[j] + c1*distribution(random)*(pbest[i].x[j] - oldparticle[i].x[j]) + c2*distribution(random)*(gbest.x[j] - oldparticle[i].x[j]));
if (oldparticle[i].v[j] > vmax)//粒子速度越界调整
oldparticle[i].v[j] = (int)vmax;
else if (oldparticle[i].v[j] < vmin)
oldparticle[i].v[j] = (int)vmin;
oldparticle[i].x[j] += oldparticle[i].v[j];
if (oldparticle[i].x[j] > citycount)oldparticle[i].x[j] = citycount;//粒子位置越界调整
else if (oldparticle[i].x[j] < 1) oldparticle[i].x[j] = 1;
}
//粒子位置有效性调整，必须满足解空间的条件
Adjuxt_validParticle(oldparticle[i]);
oldparticle[i].fitness = Evaluate(oldparticle[i].x);
pbest[i].fitness = Evaluate(pbest[i].x);
if (oldparticle[i].fitness < pbest[i].fitness)
{
for (int j = 0; j < citycount; j++)
pbest[i].x[j] = oldparticle[i].x[j];
}//更新单个粒子的历史极值
for (int j = 0; j < citycount; j++)
gbest.x[j] = pbest[i].x[j];//更新全局极值
for (int k = 0; k < popsize && k!=i; k++)
{
if (Evaluate(pbest[k].x) < Evaluate(gbest.x))
{
for (int j = 0; j < citycount; j++)
gbest.x[j] = pbest[k].x[j];
gbest.fitness = Evaluate(gbest.x);
}
}
}
outfile << "第"<<ite+1<<"次迭代后的种群如下：" << endl;
for (int i = 0; i < popsize; i++)
{
outfile << "粒子" << i + 1 << "->";
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
outfile << oldparticle[i].x[j] << ") = " << oldparticle[i].fitness << endl;
else if (j == 0)
outfile << "f(" << oldparticle[i].x[j] << ",";
else
outfile << oldparticle[i].x[j] << ",";
}
}
std::cout << "第" <<ite+1<< "次迭代后的最好粒子：";
outfile << "第" << ite + 1 << "次迭代后的最好粒子："<<endl;
for (int j = 0; j < citycount; j++)
{
if (j == citycount - 1)
outfile << gbest.x[j] << ") = " << gbest.fitness << endl;
else if (j == 0)
outfile << "f(" << gbest.x[j] << ",";
else
outfile << gbest.x[j] << ",";
}
gbest.shuchu();
}
outfile.close();
}
};
PSO pso;
int main()
{
system("mode con cols=200");//改变宽高
system("color fc");//改变颜色
std::cout << "粒子群优化算法求解TSP旅行商问题" << endl;
pso.PSO_TSP(30,500,2,2,0.8,3.0, "E:\\计算智能代码\\PSO_TSP\\PSO_TSP\\bayg29.tsp");
system("pause");
return 0;
}