1+ import numpy as np
2+ import math
3+ import time
4+
5+ def load_data (data_path ):
6+ """
7+ 导入数据，得到城市坐标信息
8+ :param data_path: 数据文件地址 str
9+ :return: 所有城市的坐标信息 二维 list
10+ """
11+ cities = []
12+ with open (data_path , 'r' ) as f :
13+ lines = f .readlines ()
14+ for line in lines :
15+ x_str , y_str = line .split ()[1 :]
16+ x , y = int (x_str ), int (y_str )
17+ cities .append ((x , y ))
18+ return cities
19+
20+ def get_cities_distance (cities ):
21+ """
22+ 计算两两城市的距离
23+ :param cities: 所有城市的坐标 二维 list
24+ :return: 城市距离矩阵 numpy数组
25+ """
26+ dist_matrix = np .zeros ((127 , 127 ))
27+ n_cities = len (cities )
28+ for i in range (n_cities - 1 ):
29+ for j in range (i + 1 , n_cities ):
30+ dist = get_two_cities_dist (cities [i ], cities [j ])
31+ dist_matrix [i , j ] = dist
32+ dist_matrix [j , i ] = dist
33+ return dist_matrix
34+
35+ def get_two_cities_dist (city1 , city2 ):
36+ """
37+ 计算两个城市的距离
38+ :param city1: 第一个城市 长度为2的list
39+ :param city2: 第二个城市 长度为2的list
40+ :return: 两城市的距离 double
41+ """
42+ x_1 , y_1 = city1
43+ x_2 , y_2 = city2
44+ return math .sqrt (math .pow (x_1 - x_2 , 2 ) + math .pow (y_1 - y_2 , 2 ))
45+
46+ def get_route_fitness_value (route , dist_matrix ):
47+ """
48+ 计算某一路线的适应度
49+ :param route: 路线 长度为城市个数的 ndarray
50+ :param dist_matrix: 距离矩阵 ndarray
51+ :return: 路线的适应度 double
52+ """
53+ dist_sum = 0
54+ for i in range (len (route )- 1 ):
55+ dist_sum += dist_matrix [route [i ], route [i + 1 ]]
56+ dist_sum += dist_matrix [route [- 1 ], route [0 ]]
57+ return 1 / dist_sum
58+
59+ def get_all_routes_fitness_value (routes , dist_matrix ):
60+ """
61+ 计算所有路线的适应度
62+ :param routes: 所有路线 ndarray
63+ :param dist_matrix: 距离矩阵 ndarray
64+ :return: 所有路线的适应度 ndarray
65+ """
66+ fitness_values = np .zeros (len (routes ))
67+ for i in range (len (routes )):
68+ f_value = get_route_fitness_value (routes [i ], dist_matrix )
69+ fitness_values [i ] = f_value
70+ return fitness_values
71+
72+ def init_route (n_route , n_cities ):
73+ """
74+ 随机初始化路线
75+ :param n_route: 初始化的路线数量 int
76+ :param n_cities: 城市的数量 int
77+ :return: 路线矩阵 二维ndarray
78+ """
79+ routes = np .zeros ((n_route , n_cities )).astype (int )
80+ for i in range (n_route ):
81+ routes [i ] = np .random .choice (range (n_cities ), size = n_cities , replace = False )
82+ return routes
83+
84+ def selection (routes , fitness_values ):
85+ """
86+ 选择操作
87+ :param routes: 所有路线 ndarray
88+ :param fitness_values: 所有路线的适应度 ndarray
89+ :return: 选择后的所有路线 ndarray
90+ """
91+ selected_routes = np .zeros (routes .shape ).astype (int )
92+ probability = fitness_values / np .sum (fitness_values )
93+ n_routes = routes .shape [0 ]
94+ for i in range (n_routes ):
95+ choice = np .random .choice (range (n_routes ), p = probability )
96+ selected_routes [i ] = routes [choice ]
97+ return selected_routes
98+
99+ def crossover (routes , n_cities ):
100+ """
101+ 交叉操作
102+ :param routes: 所有路线 ndarray
103+ :param n_cities: 城市数量 int
104+ :return: 交叉后的所有路线 ndarray
105+ """
106+ for i in range (0 , len (routes ), 2 ):
107+ r1_new , r2_new = np .zeros (n_cities ), np .zeros (n_cities )
108+ seg_point = np .random .randint (0 , n_cities )
109+ cross_len = n_cities - seg_point
110+ r1 , r2 = routes [i ], routes [i + 1 ]
111+ r1_cross , r2_cross = r2 [seg_point :], r1 [seg_point :]
112+ r1_non_cross = r1 [np .in1d (r1 , r1_cross )== False ]
113+ r2_non_cross = r2 [np .in1d (r2 , r2_cross )== False ]
114+ r1_new [:cross_len ], r2_new [:cross_len ] = r1_cross , r2_cross
115+ r1_new [cross_len :], r2_new [cross_len :] = r1_non_cross , r2_non_cross
116+ routes [i ], routes [i + 1 ] = r1_new , r2_new
117+ return routes
118+
119+ def mutation (routes , n_cities ):
120+ """
121+ 变异操作，变异概率为 0.01
122+ :param routes: 所有路线 ndarray
123+ :param n_cities: 城市数量 int
124+ :return: 变异后的所有路线 ndarray
125+ """
126+ prob = 0.01
127+ p_rand = np .random .rand (len (routes ))
128+ for i in range (len (routes )):
129+ if p_rand [i ] < prob :
130+ mut_position = np .random .choice (range (n_cities ), size = 2 , replace = False )
131+ l , r = mut_position [0 ], mut_position [1 ]
132+ routes [i , l ], routes [i , r ] = routes [i , r ], routes [i , l ]
133+ return routes
134+
135+ if __name__ == '__main__' :
136+ start = time .time ()
137+
138+ n_routes = 100 # 路线
139+ epoch = 100000 # 迭代次数
140+
141+ cities = load_data ('./cities.txt' ) # 导入数据
142+ dist_matrix = get_cities_distance (cities ) # 计算城市距离矩阵
143+ routes = init_route (n_routes , dist_matrix .shape [0 ]) # 初始化所有路线
144+ fitness_values = get_all_routes_fitness_value (routes , dist_matrix ) # 计算所有初始路线的适应度
145+ best_index = fitness_values .argmax ()
146+ best_route , best_fitness = routes [best_index ], fitness_values [best_index ] # 保存最优路线及其适应度
147+
148+ # 开始迭代
149+ not_improve_time = 0
150+ for i in range (epoch ):
151+ routes = selection (routes , fitness_values ) # 选择
152+ routes = crossover (routes , len (cities )) # 交叉
153+ routes = mutation (routes , len (cities )) # 变异
154+ fitness_values = get_all_routes_fitness_value (routes , dist_matrix )
155+ best_route_index = fitness_values .argmax ()
156+ if fitness_values [best_route_index ] > best_fitness :
157+ not_improve_time = 0
158+ best_route , best_fitness = routes [best_route_index ], fitness_values [best_route_index ] # 保存最优路线及其适应度
159+ else :
160+ not_improve_time += 1
161+ if (i + 1 ) % 200 == 0 :
162+ print ('epoch: {}, 当前最优路线距离： {}' .format (i + 1 , 1 / get_route_fitness_value (best_route , dist_matrix )))
163+ if not_improve_time >= 2000 :
164+ print ('连续2000次迭代都没有改变最优路线，结束迭代' )
165+ break
166+
167+ print ('最优路线为：' )
168+ print (best_route )
169+ print ('总距离为： {}' .format (1 / get_route_fitness_value (best_route , dist_matrix )))
170+
171+ end = time .time ()
172+ print ('耗时: {}s' .format (end - start ))
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