经典的TSP问题，是通过随机初始化蚂蚁的起始地点，然后设置每个城市都可以访问，访问完所有的城市那么结束循环，来形成回路的。
带有起始点的TSP问题就是，初始化时蚂蚁的初始点只能是起点，并且如果没访问的城市还有两个或者以上那么就设置终点不可访问（当访问的城市只剩最后一个时候打开即可，我的程序中是设置open_table的布尔值）。
所以带有起点和终点的TSP问题相对于经典的TSP问题使用蚁群算法进行求解的时候只用改两行代码即可，非常的简单。
这个蚁群算法是使用op2优化（邻域搜索优化）的蚁群，基本上100个城市的规模使用30个蚂蚁一次循环在10s内就可以得到最优值/次优解，所谓邻域搜索+蚁群算法也很简单，就是在一只蚂蚁算出所有路径之后，对子路径进行翻转即可（不懂的用笔验算一下就明白了），翻转操作用程序实现非常简单。
作者：VanJordan
链接：https://www.jianshu.com/p/a8acd65aba79
来源：简书
著作权归作者所有。商业转载请联系作者获得授权，非商业转载请注明出处。
import numpy as np
import matplotlib.pyplot as plt
import random
import copy
import time
import sys
import math
import datetime
from math import radians, cos, sin, asin, sqrt
class Ant(object):
# 初始化
def __init__(self,ID,distance_graph,pheromone_graph,ALPHA,BETA):
self.city_num=len(distance_graph)
self.distance_graph=distance_graph #距离矩阵
self.pheromone_graph=pheromone_graph #信息素矩阵
self.ID = ID # ID
(self.ALPHA, self.BETA) = (ALPHA , BETA)#蚂蚁在选择路径时 信息素与距离反比的比重
self.path = [] # 当前蚂蚁的路径
self.total_distance = 0.0 # 当前路径的总距离
self.move_count = 0 # 移动次数
self.current_city = -1 # 当前停留的城市
self.open_table_city = [True for i in range(self.city_num)] # 探索城市的状态
if self.city_num >2: #如果商店数目大于2那么就不能走city[1]
self.open_table_city[1]=False
#city_index = random.randint(0, self.city_num - 1) # 随机初始出生点
city_index=0 #初始点是开始点
self.current_city = city_index
self.path.append(city_index) # 这只蚂蚁经过的路径
self.open_table_city[city_index] = False # 城市是否无访问
self.move_count = 1
# 选择下一个城市
def _choice_next_city(self):
next_city = -1
select_citys_prob = [0.0 for i in range(self.city_num)] #选择城市的可能性
total_prob = 0.0
# 获取去下一个城市的概率
for i in range(self.city_num):
if self.open_table_city[i]:
try:
# 计算概率：与信息素浓度成正比，与距离成反比
select_citys_prob[i] = pow(self.pheromone_graph[self.current_city][i], self.ALPHA) * pow(
(1.0 / (self.distance_graph[self.current_city][i]+0.00001)), self.BETA)
total_prob += select_citys_prob[i]
except ZeroDivisionError as e:
print('Ant ID: {ID}, current city: {current}, target city: {target}'.format(ID=self.ID,current=self.current_city,target=i))
sys.exit(1)
# 轮盘选择城市
if total_prob > 0.0:
# 产生一个随机概率
temp_prob = random.uniform(0.0, total_prob)
for i in range(self.city_num):
if self.open_table_city[i]:#如果城市没有被访问
# 轮次相减
temp_prob -= select_citys_prob[i]
if temp_prob < 0.0:
next_city = i
break
# 未从概率产生，顺序选择一个未访问城市 如果temp_prob恰好选择了total_prob那么就在所有未去的城市中选择一个去的城市
if next_city == -1:
for i in range(self.city_num):
if self.open_table_city[i]:
next_city = i
break
# 返回下一个城市序号
return next_city
# 移动操作
def _move(self, next_city):
self.path.append(next_city)
self.open_table_city[next_city] = False
self.current_city = next_city
self.move_count += 1
#翻转操作
def _reverse(self,start,end):#表示是protect函数
#self.path[start:end+1]=self.path[end:start-1:-1] #从bc 变成cb
tmpPath=self.path.copy()
tmpPath[start:end+1]=tmpPath[end:start-1:-1]
return tmpPath
def _cal_lenth(self,path):
temp_distance = 0.0
for i in range(1, len(path)):
start, end = path[i], path[i - 1]
temp_distance += self.distance_graph[start][end]
return temp_distance
def _need_reverse(self,start,end):
tmpPath=self.path[start-1:end+2].copy()
tmpPath[1:-1]=tmpPath[-2:0:-1]
return self._cal_lenth(tmpPath) < self._cal_lenth(self.path[start-1:end+2])
# 搜索路径
def search_path(self):
# 搜素路径，遍历完所有城市为止
while self.move_count < self.city_num:
# 移动到下一个城市
next_city = self._choice_next_city()
self._move(next_city)
if self.move_count== self.city_num-1:#最后一个城市选择终点城市
self.open_table_city[1]=True
# 计算路径总长度
self.total_distance=self._cal_lenth(self.path)
i=2#步长
while i < self.city_num-1:
j=1#起始位置
while j < self.city_num-i:
if self._need_reverse(j,i+j-1):
self.path=self._reverse(j,i+j-1) #得到翻转之后的路径
self.total_distance =self._cal_lenth(self.path) #更新总长度
i=2#重做整个结果
j=1
j+=1
i+=1
class tsp(object):
def __init__(self,data_set):#data_set是所有点的经纬度坐标，label_list是这个分组的编号序列
self.cities = data_set # 商店的地址（经纬度信息）
self.maxIter = 1 #蚁群算法的最大迭代次数
self.rootNum = data_set.shape[0]#本分组的商店的数目
(self.city_num, self.ant_num) = (self.rootNum, 30)
(self.ALPHA, self.BETA, self.RHO, self.Q) = (1.0, 9.0, 0.5, 100.0)#蚁群算法参数
self.distance_graph=[[0.0 for i in range(self.city_num)] for j in range(self.city_num)]
self.pheromone_graph=[[1.0 for i in range(self.city_num)] for j in range(self.city_num)]
self.get_Dis_Pherom()#初始化距离
self.new()
def transf_Dist(self,lon1, lat1, lon2, lat2): # 经度1，纬度1，经度2，纬度2 （十进制度数）
"""
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
# 将十进制度数转化为弧度
lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])
# haversine公式
dlon = lon2 - lon1
dlat = lat2 - lat1
a = sin(dlat / 2) ** 2 + cos(lat1) * cos(lat2) * sin(dlon / 2) ** 2
c = 2 * asin(sqrt(a))
r = 6371 # 地球平均半径，单位为公里
return c * r * 1000
def get_Dis_Pherom(self):
# 初始化城市距离
for i in range(self.city_num):
for j in range(self.city_num):
self.distance_graph[i][j] =self.transf_Dist(self.cities[i,0],self.cities[i,1],self.cities[j,0],self.cities[j,1])
def new(self,evt=None):
# 初始化信息素
self.ants = [Ant(ID,self.distance_graph,self.pheromone_graph,self.ALPHA, self.BETA) for ID in range(self.ant_num)] # 初始蚁群
self.best_ant = self.ants[-1] # 初始最优解
self.best_ant.total_distance = (1 << 31) # 初始最大距离
self.iter = 0 # 初始化迭代次数
def search_path(self,evt=None):
while self.iter<self.maxIter:
# 遍历每一只蚂蚁
for ant in self.ants:
# 搜索一条路径
ant.search_path()
# 与当前最优蚂蚁比较
if ant.total_distance < self.best_ant.total_distance:
# 更新最优解
self.best_ant = copy.deepcopy(ant)
# 更新信息素
self.update_pheromone_gragh()
#print("迭代次数：", self.iter, u"最佳路径总距离：", int(self.best_ant.total_distance))
#self.draw()
self.iter += 1
#self.draw()
return self.best_ant.path
def update_pheromone_gragh(self):
# 获取每只蚂蚁在其路径上留下的信息素
temp_pheromone = [[0.0 for col in range(self.city_num)] for raw in range(self.city_num)]
for ant in self.ants:
for i in range(1, self.city_num):
start, end = ant.path[i - 1], ant.path[i]
# 在路径上的每两个相邻城市间留下信息素，与路径总距离反比
temp_pheromone[start][end] += self.Q / ant.total_distance
temp_pheromone[end][start] = temp_pheromone[start][end]
# 更新所有城市之间的信息素，旧信息素衰减加上新迭代信息素
for i in range(self.city_num):
for j in range(self.city_num):
self.pheromone_graph[i][j] = self.pheromone_graph[i][j] * self.RHO + temp_pheromone[i][j]
def draw_line(cities,bestPath):
city_num=cities.shape[0]
ax = plt.subplot(111)
ax.plot(cities[:, 0], cities[:, 1], 'x', color='blue')
ax.plot(cities[0,0],cities[0,1],'ro')
ax.plot(cities[1, 0], cities[1, 1], 'ro')
for i in range(city_num):
ax.text(cities[i, 0], cities[i, 1], str(i))
ax.plot(cities[bestPath, 0], cities[bestPath, 1], color='red')
plt.show()
def notInList(lon,lat,pointList):
for i in range(0,len(pointList)):
if abs(lon-pointList[i][0])<=0.000001 and abs(lat-pointList[i][1])<=0.000001:
return i
return len(pointList)
def get_route(startlon,startlat,endlon,endlat,pointdarry):
pointList=pointdarry.tolist()
listLen=len(pointList)
sameIndex=notInList(startlon,startlat,pointList)
if sameIndex < listLen:
pointList.pop(sameIndex)
sameIndex = notInList(endlon, endlat, pointList)
if sameIndex < listLen:
pointList.pop(sameIndex)
coordinateList=[[startlon,startlat],[endlon, endlat]]
coordinateList+=pointList
dataSet=np.array(coordinateList)
pathList = tsp(dataSet).search_path()
draw_line(dataSet, pathList)
resultList=[]
for i in range(len(pathList)):
if i>0 :
if coordinateList[pathList[i]][0]==coordinateList[pathList[i-1]][0] and coordinateList[pathList[i]][1]==coordinateList[pathList[i-1]][1]:
continue
else :
resultList.append(coordinateList[pathList[i]])
else :
resultList.append(coordinateList[pathList[i]])
return resultList
if __name__ == '__main__':
point_num = 66 # 点的数目
random.seed(point_num)
data_set = np.array( # 生成point_num个随机的经纬坐标信息
[[(random.random() * 100000 + 116300000) / 1000000, (random.random() * 100000 + 39900000) / 1000000] for i in
range(point_num)])
#其中第0个点是起点，第1个点是终点
resultList=get_route(116.37494599868327, 39.905368158173204, 116.36079610914554, 39.93572462665125,data_set)
print(resultList)
print(len(resultList))