#include<iostream>
#include<math.h>
#include<time.h>
using namespace std;
//该程序是以蚁群系统为模型写的蚁群算法程序(强调：非蚂蚁周模型)，以三个著名的TSP问题为测试对象
//通过微调参数，都可以获得较好的解
/*
//———-(1)问题一：Oliver 30 城市 TSP 问题 best_length = 423.7406; ————————
//该程序最好的结果是423.741，可运行多次获得
//城市节点数目
#define N 30
//城市坐标
double C[N][2]={
{2,99},{4,50},{7,64},{13,40},{18,54},{18,40},{22,60},{24,42},{25,62},{25,38},
{37,84},{41,94},{41,26},{44,35},{45,21},{54,67},{54,62},{58,35},{58,69},{62,32},
{64,60},{68,58},{71,44},{71,71},{74,78},{82,7},{83,46},{83,69},{87,76},{91,38}
};
//———-上面参数是固定的，下面的参数是可变的———–
//蚂蚁数量
#define M 30
//最大循环次数NcMax
int NcMax = 500;
//信息启发因子，期望启发式因子，全局信息素挥发参数，局部信息素挥发参数, 状态转移公式中的q0
double alpha = 2, beta = 3, rou = 0.1, alpha1 = 0.1, qzero = 0.01;
//———–问题一结束————————————————————————
*/
/*
//———-(2)问题二：Elion50 城市 TSP 问题 best_length = 427.96; —————————-
//该程序最好的结果是428.468，可运行多次获得
//城市节点数目
#define N 50
//城市坐标
double C[N][2]={
{5,64}, {5,25}, {5,6}, {7,38}, {8,52}, {10,17},
{12,42}, {13,13}, {16,57}, {17,33}, {17,63},
{20,26}, {21,47}, {21,10}, {25,32}, {25,55},
{27,68}, {27,23}, {30,48}, {30,15}, {31,62},
{31,32}, {32,22}, {32,39}, {36,16}, {37,69},
{37,52}, {38,46}, {39,10}, {40,30}, {42,57},
{42,41}, {43,67}, {45,35}, {46,10}, {48,28},
{49,49}, {51,21}, {52,33}, {52,41}, {52,64},
{56,37}, {57,58}, {58,27}, {58,48}, {59,15},
{61,33}, {62,42}, {62,63}, {63,69}
};
//———-上面参数是固定的，下面的参数是可变的———–
//蚂蚁数量
#define M 50
//最大循环次数NcMax
int NcMax = 1000;
//信息启发因子，期望启发式因子，全局信息素挥发参数，局部信息素挥发参数, 状态转移公式中的q0
double alpha = 2, beta = 4, rou = 0.1, alpha1 = 0.1, qzero = 0.01;
//———–问题二结束————————————————————————
*/
//———-(3)问题三：Elion75 城市 TSP 问题 best_length = 542.31;
//该程序最好的结果是542.309，可运行多次获得
//城市节点数目
#define N 75
//城市坐标
double C[N][2]={
{6,25}, {7,43}, {9,56}, {10,70}, {11,28},
{12,17}, {12,38}, {15,5}, {15,14}, {15,56},
{16,19}, {17,64}, {20,30}, {21,48}, {21,45},
{21,36}, {22,53}, {22,22}, {26,29}, {26,13},
{26,59}, {27,24}, {29,39}, {30,50}, {30,20},
{30,60}, {31,76}, {33,34}, {33,44}, {35,51},
{35,16}, {35,60}, {36,6}, {36,26}, {38,33},
{40,37}, {40,66}, {40,60}, {40,20}, {41,46},
{43,26}, {44,13}, {45,42}, {45,35}, {47,66},
{48,21}, {50,30}, {50,40}, {50,50}, {50,70},
{50,4}, {50,15}, {51,42}, {52,26}, {54,38},
{54,10}, {55,34}, {55,45}, {55,50}, {55,65},
{55,57}, {55,20}, {57,72}, {59,5}, {60,15},
{62,57}, {62,48}, {62,35}, {62,24}, {64,4},
{65,27}, {66,14}, {66,8}, {67,41}, {70,64}
};
//———-上面参数是固定的，下面的参数是可变的———–
//蚂蚁数量
#define M 75
//最大循环次数NcMax
int NcMax =1000;
//信息启发因子，期望启发式因子，全局信息素挥发参数，局部信息素挥发参数, 状态转移公式中的q0
double alpha = 2, beta = 5, rou = 0.1, alpha1 = 0.1, qzero = 0.1;
//———–问题三结束————————————————————————
//===========================================================================================================
//局部更新时候使用的的常量，它是由最近邻方法得到的一个长度
//什么是最近邻方法?:)就是从源节点出发，每次选择一个距离最短的点来遍历所有的节点得到的路径
//每个节点都可能作为源节点来遍历
double Lnn;
//矩阵表示两两城市之间的距离
double allDistance[N][N];
//计算两个城市之间的距离
double calculateDistance(int i, int j)
{
return sqrt(pow((C[i][0]-C[j][0]),2.0) + pow((C[i][1]-C[j][1]),2.0));
}
//由矩阵表示两两城市之间的距离
void calculateAllDistance()
{
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
if (i != j)
{
allDistance[i][j] = calculateDistance(i, j);
allDistance[j][i] = allDistance[i][j];
}
}
}
}
//获得经过n个城市的路径长度
double calculateSumOfDistance(int* tour)
{
double sum = 0;
for(int i = 0; i< N ;i++)
{
int row = *(tour + 2 * i);
int col = *(tour + 2* i + 1);
sum += allDistance[row][col];
}
return sum;
}
class ACSAnt;
class AntColonySystem
{
private:
double info[N][N], visible[N][N];//节点之间的信息素强度,节点之间的能见度
public:
AntColonySystem()
{
}
//计算当前节点到下一节点转移的概率
double Transition(int i, int j);
//局部更新规则
void UpdateLocalPathRule(int i, int j);
//初始化
void InitParameter(double value);
//全局信息素更新
void UpdateGlobalPathRule(int* bestTour, int globalBestLength);
};
//计算当前节点到下一节点转移的概率
double AntColonySystem::Transition(int i, int j)
{
if (i != j)
{
return (pow(info[i][j],alpha) * pow(visible[i][j], beta));
}
else
{
return 0.0;
}
}
//局部更新规则
void AntColonySystem::UpdateLocalPathRule(int i, int j)
{
info[i][j] = (1.0 – alpha1) * info[i][j] + alpha1 * (1.0 / (N * Lnn));
info[j][i] = info[i][j];
}
//初始化
void AntColonySystem::InitParameter(double value)
{
//初始化路径上的信息素强度tao0
for(int i = 0; i < N; i++)
{
for(int j = 0; j < N; j++)
{
info[i][j] = value;
info[j][i] = value;
if (i != j)
{
visible[i][j] = 1.0 / allDistance[i][j];
visible[j][i] = visible[i][j];
}
}
}
}
//全局信息素更新
void AntColonySystem::UpdateGlobalPathRule(int* bestTour, int globalBestLength)
{
for(int i = 0; i < N; i++)
{
int row = *(bestTour + 2 * i);
int col = *(bestTour + 2* i + 1);
info[row][col] = (1.0 – rou) * info[row][col] + rou * (1.0 / globalBestLength);
info[col][row] =info[row][col];
}
}
class ACSAnt
{
private:
AntColonySystem* antColony;
protected:
int startCity, cururentCity;//初始城市编号，当前城市编号
int allowed[N];//禁忌表
int Tour[N][2];//当前路径
int currentTourIndex;//当前路径索引，从0开始，存储蚂蚁经过城市的编号
public:
ACSAnt(AntColonySystem* acs, int start)
{
antColony = acs;
startCity = start;
}
//开始搜索
int* Search();
//选择下一节点
int Choose();
//移动到下一节点
void MoveToNextCity(int nextCity);
};
//开始搜索
int* ACSAnt::Search()
{
cururentCity = startCity;
int toCity;
currentTourIndex = 0;
for(int i = 0; i < N; i++)
{
allowed[i] = 1;
}
allowed[cururentCity] = 0;
int endCity;
int count = 0;
do
{
count++;
endCity = cururentCity;
toCity = Choose();
if (toCity >= 0)
{
MoveToNextCity(toCity);
antColony->UpdateLocalPathRule(endCity, toCity);
cururentCity = toCity;
}
}while(toCity >= 0);
MoveToNextCity(startCity);
antColony->UpdateLocalPathRule(endCity, startCity);
return *Tour;
}
//选择下一节点
int ACSAnt::Choose()
{
int nextCity = -1;
double q = rand()/(double)RAND_MAX;
//如果 q <= q0,按先验知识，否则则按概率转移，
if (q <= qzero)
{
double probability = -1.0;//转移到下一节点的概率
for(int i = 0; i < N; i++)
{
//去掉禁忌表中已走过的节点,从剩下节点中选择最大概率的可行节点
if (1 == allowed[i])
{
double prob = antColony->Transition(cururentCity, i);
if (prob > probability)
{
nextCity = i;
probability = prob;
}
}
}
}
else
{
//按概率转移
double p = rand()/(double)RAND_MAX;//生成一个随机数,用来判断落在哪个区间段
double sum = 0.0;
double probability = 0.0;//概率的区间点，p 落在哪个区间段，则该点是转移的方向
//计算概率公式的分母的值
for(int i = 0; i < N; i++)
{
if (1 == allowed[i])
{
sum += antColony->Transition(cururentCity, i);
}
}
for(int j = 0; j < N; j++)
{
if (1 == allowed[j] && sum > 0)
{
probability += antColony->Transition(cururentCity, j)/sum;
if (probability >= p || (p > 0.9999 && probability > 0.9999))
{
nextCity = j;
break;
}
}
}
}
return nextCity;
}
//移动到下一节点
void ACSAnt::MoveToNextCity(int nextCity)
{
allowed[nextCity]=0;
Tour[currentTourIndex][0] = cururentCity;
Tour[currentTourIndex][1] = nextCity;
currentTourIndex++;
cururentCity = nextCity;
}
//——————————————
//选择下一个节点，配合下面的函数来计算的长度
int ChooseNextNode(int currentNode, int visitedNode[])
{
int nextNode = -1;
double shortDistance = 0.0;
for(int i = 0; i < N; i++)
{
//去掉已走过的节点,从剩下节点中选择距离最近的节点
if (1 == visitedNode[i])
{
if (shortDistance == 0.0)
{
shortDistance = allDistance[currentNode][i];
nextNode = i;
}
if(shortDistance < allDistance[currentNode][i])
{
nextNode = i;
}
}
}
return nextNode;
}
//给一个节点由最近邻距离方法计算长度
double CalAdjacentDistance(int node)
{
double sum = 0.0;
int visitedNode[N];
for(int j = 0; j < N; j++)
{
visitedNode[j] = 1;
}
visitedNode[node] = 0;
int currentNode = node;
int nextNode;
do
{
nextNode = ChooseNextNode(currentNode, visitedNode);
if (nextNode >= 0)
{
sum += allDistance[currentNode][nextNode];
currentNode= nextNode;
visitedNode[currentNode] = 0;
}
}while(nextNode >= 0);
sum += allDistance[currentNode][node];
return sum;
}
//———————————结束———————————————
//————————–主函数————————————————–
int main()
{
time_t timer,timerl;
time(&timer);
unsigned long seed = timer;
seed %= 56000;
srand((unsigned int)seed);
//由矩阵表示两两城市之间的距离
calculateAllDistance();
//蚁群系统对象
AntColonySystem* acs = new AntColonySystem();
ACSAnt* ants[M];
//蚂蚁均匀分布在城市上
for(int k = 0; k < M; k++)
{
ants[k] = new ACSAnt(acs, (int)(k%N));
}
calculateAllDistance();
//随机选择一个节点计算由最近邻方法得到的一个长度
int node = rand() % N;
Lnn = CalAdjacentDistance(node);
//各条路径上初始化的信息素强度
double initInfo = 1 / (N * Lnn);
acs->InitParameter(initInfo);
//全局最优路径
int globalTour[N][2];
//全局最优长度
double globalBestLength = 0.0;
for(int i = 0; i < NcMax; i++)
{
//局部最优路径
int localTour[N][2];
//局部最优长度
double localBestLength = 0.0;
//当前路径长度
double tourLength;
for(int j = 0; j < M; j++)
{
int* tourPath = ants[j]->Search();
tourLength = calculateSumOfDistance(tourPath);
//局部比较，并记录路径和长度
if(tourLength < localBestLength || abs(localBestLength – 0.0) < 0.000001)
{
for(int m = 0; m< N; m++)
{
int row = *(tourPath + 2 * m);
int col = *(tourPath + 2* m + 1);
localTour[m][0] = row;
localTour[m][1] = col;
}
localBestLength = tourLength;
}
}
//全局比较，并记录路径和长度
if(localBestLength < globalBestLength || abs(globalBestLength – 0.0) < 0.000001)
{
for(int m = 0; m< N; m++)
{
globalTour[m][0] = localTour[m][0];
globalTour[m][1] = localTour[m][1];
}
globalBestLength = localBestLength;
}
acs->UpdateGlobalPathRule(*globalTour, globalBestLength);
//输出所有蚂蚁循环一次后的迭代最优路径
cout<<“第 “<<i + 1<<” 迭代最优路径:”<<localBestLength<<“.”<<endl;
for(int m = 0; m< N; m++)
{
cout<<localTour[m][0]<<“.”;
}
cout<<endl;
}
//输出全局最优路径
cout<<“全局最优路径长度:”<<globalBestLength<<endl;
cout<<“全局最优路径:”;
for(int m = 0; m< N; m++)
{
cout<<globalTour[m][0]<<“.”;
}
cout<<endl;
time(&timerl);
int t = timerl – timer;
return 0;
}
//————————–主函数结束————————————————–
