C++实现
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include <time.h>
//对于精度要求为小数点后1位的，下界可以取1e-3或1e-4，降温系数取 0.8 ；对于精度要求为1e-5 , 下界可取1e-7或1e-8 ,降温系数取 0.98。
#define//初始温度
#define//结束温度
#define//退火系数
#define//每个温度最大迭代次数
#define//城市个数
int city_result[N]; //城市列表的解空间
double city[N][2] = { {9932, 4439}, {10109, 4351}, {11552, 3472}, {10302, 3290}, {8776, 3333}, {7040, 4867}, {9252, 4278}, {9395, 4539}, {11101, 2540}, {9825, 5087}, {10047, 4879}, {10227, 4648}, {100027, 4229}, {9878, 4211}, {9087, 4065}, {10438, 4075}, {10382, 3865}, {11196, 3563}, {11075, 3543}, {11544, 3365}, {11915, 2900}, {11305, 3189}, {11073, 3137}, {10950, 3394}, {11576, 2575}, {12239, 2785}, {11529, 2226}, {9328, 4006}, {10012, 3811}, {9952, 3410}, {10612, 2954}, {10349, 2784}, {11747, 2469}, {11673, 2461} }; //中国34个城市实际距离坐标
//函数声明
//double city[N][2] = {{0,0},{3,0},{3,4}};//测试数据
double distance(double* city1, double* city2); //计算两城市间距离
double path(int city_result[N]); //计算总路径
void init(); //初始化解空间
void creat(); //生成新的解空间
int main()
{
time_t start, end; //记录程序开始结束时间
double time_sum; //记录程序运行时间
start = clock(); //程序开始时间
int i, count=0; //降温计数器
int city_copyresult[N]; //拷贝解空间
double path1, path2; //原有解空间，新解空间的总路径
double dE; //原有解空间与新解空间的差值
double r; //随机产生0~1的值，是否接受新的解
double T; //当前温度
srand(time(NULL));
init(); //初始化解空间
T = T_start;//初始温度赋值
while (T > T_end) //当前温度大于结束温度
{
for (i = 0; i < L; i++)
{
memcpy(city_copyresult, city_result, N * sizeof(int));
creat(); //产生新的解空间
path1 = path(city_copyresult);
path2 = path(city_result);
dE = path2 - path1;
if (dE > 0) //Metropolis准则
{
r = rand() / (RAND_MAX);
if (exp(-dE / T) <= r) //高温状态下，可以接受能量差值较大的新状态；低温状态下，则只能接受能量差值较小的新状态
memcpy(city_result, city_copyresult, N * sizeof(int)); //保留原来的解
}
}
T *= q;
count++;
}
end = clock(); //程序结束时间
time_sum = (double)(end - start) / (CLOCKS_PER_SEC); //换算成秒
printf("共降温：%d次\n", count);
printf("经过模拟退火算法得出最优路径长度为：%f\n", path(city_result));
for (i = 0; i < N; i++)
{
printf("%d->", city_result[i]);
}
printf("%d\n", city_result[0]);
printf("程序共耗时%f秒.\n", time_sum);
system("pause");
return 0;
}
double distance(double* city1, double* city2) //计算两个城市之间的距离
{
double x1, x2, y1, y2, dis;
x1 = *city1; //第一个城市的x坐标
x2 = *city2; //第二个城市的x坐标
y1 = *(city1 + 1); //第一个城市的y坐标
y2 = *(city2 + 1); //第二个城市的y坐标
dis = sqrt(pow((x2 - x1), 2) + pow((y2 - y1), 2));
return dis;
}
double path(int city_result[N]) //计算总路径
{
int i, city1_num, city2_num; //解空间中的两个城市序号
double sum = 0; //路径总长度
for (i = 0; i < N - 1; i++) //解空间中首位到末位的总路径
{
city1_num = city_result[i];
city2_num = city_result[i + 1];
sum += distance(city[city1_num], city[city2_num]);
}
sum += distance(city[0], city[N - 1]); //加上解空间中末位到首位的路径
return sum;
}
void init() //初始化解空间
{
int i;
for (i = 0; i < N; i++)
city_result[i] = i; //顺序生成解空间
}
void creat() //生成新的解空间
{
int point1, point2, temp;
point1 = rand() % N;
point2 = rand() % N;
temp = city_result[point1];
city_result[point1] = city_result[point2];
city_result[point2] = temp;
}
C#实现
using System;
using System.Collections.Generic;
namespace ConsoleApp1
{
class Point
{
public double x;
public double y;
public Point(double i,double j)
{
x = i;y = j;
}
}
class 退火算法模拟
{
private double T_start =5000.0; //初始温度
private double T_end =(1e-8) ; //结束温度
private double q =0.98 ; //退火系数
private double L =1000 ; //每个温度最大迭代次数
private static int N = 0 ; //城市个数
private List<int> city_result = new List<int>(N);//城市列表的解空间,即下标
private static List<Point> city = new List<Point>(N);//城市实际距离坐标
public 退火算法模拟(List<Point> plist)
{
N = plist.Count;
city_result = new List<int>(N);
for(int i = 0; i < N; i++)
{
city_result.Add(i);
}
city = plist;
//Console.WriteLine(city_result.Count);
}
private static double distance(Point p1,Point p2)
{
return Math.Sqrt((p1.x-p2.x)* (p1.x - p2.x) + (p1.y - p2.y)* (p1.y - p2.y));
}
private static double pathSum(List<int> list)
{
int city1_num, city2_num;//解空间中的两个城市序号
double sum = 0.0;
for(int i = 0; i < list.Count; i++)
{
city1_num = list[i];
city2_num = list[(i+1)%list.Count];
sum += distance( city[i] , city[(i+1)%list.Count] );
}
return sum;
}
private void createNewValue()//就是随机打乱
{
int p1, p2;
Random r = new Random();
p1 = r.Next(N);
p2 = r.Next(N);
var temp = city_result[p1];
city_result[p1] = city_result[p2];
city_result[p2] = temp;
}
private List<Point> returnList(List<Point> plist,List<int> list)
{
List<Point> resultList = new List<Point>(plist.Count);
foreach (var index in list)
{
resultList.Add(plist[index]);
}
return resultList;
}
public List<Point> mainAlgorithm()
{
int count=0,i=0;//降温计数器
List<int> city_result_Copy = new List<int>(N);
double path1, path2; //原有解空间，新解空间的总路径
double dE; //原有解空间与新解空间的差值
double r; //随机产生0~1的值，是否接受新的解
double T; //当前温度
T = T_start;//初始温度赋值
Random random = new Random();
DateTime start = System.DateTime.Now;
while (T >T_end)
{
for (i = 0; i < L; i++)
{
city_result_Copy.Clear();
city_result_Copy.AddRange(city_result);
createNewValue();
path1 = pathSum(city_result_Copy);
path2 = pathSum(city_result);
dE = path1 - path2;
if(dE > 0)
{
//Metropolis准则：若Δt′< 0则接受S′作为新的当前解S，
// 否则以概率exp（-Δt′/ T）接受S′作为新的当前解S。
r = random.NextDouble();
if( Math.Exp(-dE/T) <= r)//高温状态下，可以接受能量差值较大的新状态；低温状态下，则只能接受能量差值较小的新状态
{//保留原来的解
city_result.Clear();
city_result.AddRange(city_result_Copy);
}
}
}
T *= q;
count++;
}
DateTime end = System.DateTime.Now;
Console.WriteLine("花费的时间为{0},降温次数{1}", (end - start) ,count);
List<Point> resultList = new List<Point>(city.Count);
resultList=returnList(city, city_result);
return resultList;
}
static void Main(string[] args)
{
double[,] city = new double[34, 2] { { 9932, 4439 }, { 10109, 4351 }, { 11552, 3472 }, { 10302, 3290 }, { 8776, 3333 }, { 7040, 4867 }, { 9252, 4278 }, { 9395, 4539 }, { 11101, 2540 }, { 9825, 5087 }, { 10047, 4879 }, { 10227, 4648 }, { 100027, 4229 }, { 9878, 4211 }, { 9087, 4065 }, { 10438, 4075 }, { 10382, 3865 }, { 11196, 3563 }, { 11075, 3543 }, { 11544, 3365 }, { 11915, 2900 }, { 11305, 3189 }, { 11073, 3137 }, { 10950, 3394 }, { 11576, 2575 }, { 12239, 2785 }, { 11529, 2226 }, { 9328, 4006 }, { 10012, 3811 }, { 9952, 3410 }, { 10612, 2954 }, { 10349, 2784 }, { 11747, 2469 }, { 11673, 2461 } }; //中国34个城市实际距离坐标
int num = city.GetLength(0);
List<Point> plist = new List<Point>(num);
List<Point> resultlist = new List<Point>(num);
for (int i = 0; i < num; i++)
{
Point temp = new Point(city[i, 0], city[i, 1]);
plist.Add(temp);
}
resultlist = new 退火算法模拟(plist).mainAlgorithm();
foreach (var item in resultlist)
{
Console.WriteLine(item.x + " " + item.y);
}
}
}
}
