import numpy as np
import matplotlib.pyplot as plt
# 建立“蚂蚁”类
class Ant(object):
def __init__(self, path):
self.path = path # 蚂蚁当前迭代整体路径
self.length = self.calc_length(path) # 蚂蚁当前迭代整体路径长度
def calc_length(self, path_): # path=[A, B, C, D, A]注意路径闭环
length_ = 0
for i in range(len(path_)-1):
delta = (path_[i].x - path_[i+1].x, path_[i].y - path_[i+1].y)
length_ += np.linalg.norm(delta)
return length_
@staticmethod
def calc_len(A, B): # 静态方法，计算城市A与城市B之间的距离
return np.linalg.norm((A.x - B.x, A.y - B.y))
# 建立“城市”类
class City(object):
def __init__(self, x, y):
self.x = x
self.y = y
# 建立“路径”类
class Path(object):
def __init__(self, A): # A为起始城市
self.path = [A, A]
def add_path(self, B): # 追加路径信息，方便计算整体路径长度
self.path.append(B)
self.path[-1], self.path[-2] = self.path[-2], self.path[-1]
# 构建“蚁群算法”的主体
class ACO(object):
def __init__(self, ant_num=50, maxIter=300, alpha=1, beta=5, rho=0.1, Q=1):
self.ants_num = ant_num # 蚂蚁个数
self.maxIter = maxIter # 蚁群最大迭代次数
self.alpha = alpha # 信息启发式因子
self.beta = beta # 期望启发式因子
self.rho = rho # 信息素挥发速度
self.Q = Q # 信息素强度
###########################
self.deal_data('coordinates.dat') # 提取所有城市的坐标信息
###########################
self.path_seed = np.zeros(self.ants_num).astype(int) # 记录一次迭代过程中每个蚂蚁的初始城市下标
self.ants_info = np.zeros((self.maxIter, self.ants_num)) # 记录每次迭代后所有蚂蚁的路径长度信息
self.best_path = np.zeros(self.maxIter) # 记录每次迭代后整个蚁群的“历史”最短路径长度
###########################
self.solve() # 完成算法的迭代更新
self.display() # 数据可视化展示
def deal_data(self, filename):
with open(filename, 'rt') as f:
temp_list = list(line.split() for line in f) # 临时存储提取出来的坐标信息
self.cities_num = len(temp_list) # 1. 获取城市个数
self.cities = list(City(float(item[0]), float(item[1])) for item in temp_list) # 2. 构建城市列表
self.city_dist_mat = np.zeros((self.cities_num, self.cities_num)) # 3. 构建城市距离矩阵
for i in range(self.cities_num):
A = self.cities[i]
for j in range(i, self.cities_num):
B = self.cities[j]
self.city_dist_mat[i][j] = self.city_dist_mat[j][i] = Ant.calc_len(A, B)
self.phero_mat = np.ones((self.cities_num, self.cities_num)) # 4. 初始化信息素矩阵
# self.phero_upper_bound = self.phero_mat.max() * 1.2 ###信息素浓度上限
self.eta_mat = 1/(self.city_dist_mat + np.diag([np.inf]*self.cities_num)) # 5. 初始化启发函数矩阵
def solve(self):
iterNum = 0 # 当前迭代次数
while iterNum < self.maxIter:
self.random_seed() # 使整个蚁群产生随机的起始点
delta_phero_mat = np.zeros((self.cities_num, self.cities_num)) # 初始化每次迭代后信息素矩阵的增量
##########################################################################
for i in range(self.ants_num):
city_index1 = self.path_seed[i] # 每只蚂蚁访问的第一个城市下标
ant_path = Path(self.cities[city_index1]) # 记录每只蚂蚁访问过的城市
tabu = [city_index1] # 记录每只蚂蚁访问过的城市下标，禁忌城市下标列表
non_tabu = list(set(range(self.cities_num)) - set(tabu))
for j in range(self.cities_num-1): # 对余下的城市进行访问
up_proba = np.zeros(self.cities_num-len(tabu)) # 初始化状态迁移概率的分子
for k in range(self.cities_num-len(tabu)):
up_proba[k] = np.power(self.phero_mat[city_index1][non_tabu[k]], self.alpha) * \
np.power(self.eta_mat[city_index1][non_tabu[k]], self.beta)
proba = up_proba/sum(up_proba) # 每条可能子路径上的状态迁移概率
while True: # 提取出下一个城市的下标
random_num = np.random.rand()
index_need = np.where(proba > random_num)[0]
if len(index_need) > 0:
city_index2 = non_tabu[index_need[0]]
break
ant_path.add_path(self.cities[city_index2])
tabu.append(city_index2)
non_tabu = list(set(range(self.cities_num)) - set(tabu))
city_index1 = city_index2
self.ants_info[iterNum][i] = Ant(ant_path.path).length
if iterNum == 0 and i == 0: # 完成对最佳路径城市的记录
self.best_cities = ant_path.path
else:
if self.ants_info[iterNum][i] < Ant(self.best_cities).length: self.best_cities = ant_path.path
tabu.append(tabu[0]) # 每次迭代完成后，使禁忌城市下标列表形成完整闭环
for l in range(self.cities_num):
delta_phero_mat[tabu[l]][tabu[l+1]] += self.Q/self.ants_info[iterNum][i]
self.best_path[iterNum] = Ant(self.best_cities).length
self.update_phero_mat(delta_phero_mat) # 更新信息素矩阵
iterNum += 1
def update_phero_mat(self, delta):
self.phero_mat = (1 - self.rho) * self.phero_mat + delta
# self.phero_mat = np.where(self.phero_mat > self.phero_upper_bound, self.phero_upper_bound, self.phero_mat) # 判断是否超过浓度上限
def random_seed(self): # 产生随机的起始点下表，尽量保证所有蚂蚁的起始点不同
if self.ants_num <= self.cities_num: # 蚂蚁数 <= 城市数
self.path_seed[:] = np.random.permutation(range(self.cities_num))[:self.ants_num]
else: # 蚂蚁数 > 城市数
self.path_seed[:self.cities_num] = np.random.permutation(range(self.cities_num))
temp_index = self.cities_num
while temp_index + self.cities_num <= self.ants_num:
self.path_seed[temp_index:temp_index + self.cities_num] = np.random.permutation(range(self.cities_num))
temp_index += self.cities_num
temp_left = self.ants_num % self.cities_num
if temp_left != 0:
self.path_seed[temp_index:] = np.random.permutation(range(self.cities_num))[:temp_left]
def display(self): # 数据可视化展示
plt.figure(figsize=(6, 10))
plt.subplot(211)
plt.plot(self.ants_info, 'g.')
plt.plot(self.best_path, 'r-', label='history_best')
plt.xlabel('Iteration')
plt.ylabel('length')
plt.legend()
plt.subplot(212)
plt.plot(list(city.x for city in self.best_cities), list(city.y for city in self.best_cities), 'g-')
plt.plot(list(city.x for city in self.best_cities), list(city.y for city in self.best_cities), 'r.')
plt.xlabel('x')
plt.ylabel('y')
plt.savefig('ACO.png', dpi=500)
plt.show()
plt.close()
ACO()
|
