模拟退火算法求解TSP简单实现
算法思想，模拟物理的退火过程。区别于爬山算法的关键在于，对于比当前差的解，不是直接舍弃，而是以一定的概率接受。
(主要框架：三个函数+两个准则)
给定初温t=t0，随机产生初始状态s=s0，令k=0；
Repeat
Repeat
产生新状态sj=Genete(s)；
if min{1,exp[-(C(sj)-C(s))/tk]}>=randrom[0,1] s=sj;
Until 抽样稳定准则满足；
退温tk+1=update(tk)并令k=k+1；
Until算法终止准则满足；
输出算法搜索结果。
#include <iostream>
#include <vector>
#include <iterator>
#include <algorithm>
#include <ctime>
#include <cmath>
#include <fstream>
#define CITYNUM 52
#define MAX 0x7fffffff
using namespace std;
struct Point
{
int x;
int y;
char name;
};
//read the graph & compute the distance dist[i][j]
void InitGraph(double dist[CITYNUM][CITYNUM],Point citys[CITYNUM])
{
fstream fileRead;
fileRead.open("coords.txt",ios::in);
for(int i=0;i<CITYNUM;i++)
{
int temp;
char ch;
fileRead>>temp>>ch>>citys[i].x>>ch>>citys[i].y>>ch>>citys[i].name;
//cout<<temp<<ch<<citys[i].x<<ch<<citys[i].y<<ch<<citys[i].name<<endl;
}
fileRead.close();
for(int i=0;i<CITYNUM;i++)
{
for(int j=0;j<CITYNUM;j++)
{
if(j!=i&&dist[i][j]==0)
{
double d2=(citys[i].x-citys[j].x)*(citys[i].x-citys[j].x)+(citys[i].y-citys[j].y)*(citys[i].y-citys[j].y);
dist[i][j]=dist[j][i]=sqrt(d2);
}
}
}
}
double Evalue(const vector<int> answer,double dist[CITYNUM][CITYNUM])
{
double sum=0;
for(int i=0;i<answer.size()-1;i++)
{
//cout<<answer[i]<<"->"<<answer[i+1]<<":"<<sum<<"+"<<dist[answer[i]][answer[i+1]]<<"="<<sum+dist[answer[i]][answer[i+1]]<<endl;
sum+=dist[answer[i]][answer[i+1]];
}
sum+=dist[answer[answer.size()-1]][answer[0]];
return sum;
}
void Swap(vector<int> &newAnswer,int first,int second)
{
newAnswer[first]=newAnswer[first]^newAnswer[second];
newAnswer[second]=newAnswer[first]^newAnswer[second];
newAnswer[first]=newAnswer[first]^newAnswer[second];
}
void Reverse(vector<int> &newAnswer,int first,int second)
{
if(first>second)
{
first=first^second;
second=first^second;
first=first^second;
}
reverse(newAnswer.begin()+first,newAnswer.begin()+second);
}
void Save(const vector<int> minAnswer,Point citys[CITYNUM],double t0,double alpha,double te,double minSum)
{
fstream fileWrite;
fileWrite.open("out.txt",ios::out|ios::app);
fileWrite<<"起始温度："<<t0<<"，终止温度："<<te<<"，降温系数："<<alpha<<"，近似最优："<<minSum<<endl;
for(int i=0;i<minAnswer.size();i++)
{
fileWrite<<citys[minAnswer[i]].name<<"->";
}
fileWrite<<citys[minAnswer[0]].name<<endl;
fileWrite.close();
}
void SimuAnne(double t0,double alpha,double te )
{
vector<int> answer,newAnswer,minAnswer;
int k=0;//记录循环次数
double t=t0;
double sumDist=0,newSum=0,minSum=MAX;
double dist[CITYNUM][CITYNUM]={0};
Point citys[CITYNUM];//city's coordinate
InitGraph(dist,citys);
//initial answer
for(int i=0;i<CITYNUM;i++)
{
answer.push_back(i);
}
srand ( unsigned (time(0) ) );
random_shuffle(answer.begin(),answer.end());
sumDist=Evalue(answer,dist);
minSum=sumDist;
minAnswer.assign(newAnswer.begin(),newAnswer.end());
cout<<k<<" "<<minSum<<endl;
copy(answer.begin(),answer.end(),ostream_iterator<int>(cout," "));cout<<endl;//输出answer
while(t>te)
{
//srand ( unsigned (time(0) ) );
newAnswer.assign(answer.begin(),answer.end());
int first=0,second=0;
//swap first & second
first=rand()%CITYNUM;
second=rand()%CITYNUM;
if(first!=second)
{
//cout<<first<<"--"<<second<<endl;
Swap(newAnswer,first,second);//产生新的状态
//Reverse(newAnswer,first,second);//产生新的状态
newSum=Evalue(newAnswer,dist);
if(min(1.0,exp(-(newSum-sumDist)/t))>=(rand()%998)/997.0)
{
answer.assign(newAnswer.begin(),newAnswer.end());
sumDist=newSum;
if(newSum<minSum)
{
minSum=newSum;
minAnswer.assign(newAnswer.begin(),newAnswer.end());
cout<<k<<" "<<minSum<<endl;
copy(answer.begin(),answer.end(),ostream_iterator<int>(cout," "));cout<<endl;//输出answer
}
k++;
}
t=t*alpha;
}
}
Save(minAnswer,citys,t0,alpha,te,minSum);
for(int i=0;i<minAnswer.size();i++)
{
cout<<citys[minAnswer[i]].name<<"->";
}
cout<<citys[minAnswer[0]].name<<endl;
}
int main()
{
double t0=10000000;//起始温度
double alpha=0.999999;//降温系数
double te=0.000001;//截止温度
SimuAnne(t0,alpha,te);
return 0;
}
测试数据：
0,1,1,a 1,1,2,b 2,1,3,c 3,1,4,d 4,1,5,e 5,1,6,f 6,1,7,g 7,1,8,h 8,1,9,i 9,1,10,j 10,2,11,k 11,7,11,l 12,12,11,m 13,17,11,n 14,22,11,o 15,27,11,p 16,32,11,q 17,37,11,r 18,42,11,s 19,47,11,t 20,52,11,u 21,57,11,v 22,62,11,w 23,67,11,x 24,72,11,y 25,77,11,z 26,82,11,A 27,87,11,B 28,92,11,C 29,97,11,D 30,101,10,E 31,101,9,F 32,101,8,G 33,101,7,H 34,101,6,I 35,101,5,J 36,101,4,K 37,101,3,L 38,101,2,M 39,100,1,N 40,95,1,O 41,90,1,P 42,85,1,Q 43,80,1,R 44,75,1,S 45,70,1,T 46,65,1,U 47,60,1,V 48,55,1,W 49,50,1,X 50,45,1,Y 51,40,1,Z
以上算法，循环次数比较多。跟蚁群算法一比被虐成渣（有兴趣的话可以留言交流）。
起始温度：1e+007，终止温度：1e-006，降温系数：0.999999，近似最优：228.351 t->s->r->q->p->o->n->j->i->h->g->f->e->d->c->b->a->k->l->m->Z->Y->X->W->V->U->T->S->R->Q->P->O->N->M->L->K->J->I->H->G->F->E->D->C->B->A->z->y->x->w->v->u->t