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优化了算法并补充了实验内容
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‎GTSP_instance.md

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##### 1. GTSP(9,5)
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| 物品 | 城市(编号，坐标) |
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| ----- | ----------------------------------------- |
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| 物品1 | [[0,[78, 34]], [1,[16, 56]] |
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| 物品2 | [[2,[98, 23]] |
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| 物品3 | [[3,[34, 15]], [4,[79, 46]], [5,[67,51]] |
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| 物品4 | [[6,[86, 13]], [7,[99, 46]] |
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| 物品5 | [[8,[47, 83]] |
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##### 2. GTSP（17,11）
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| 物品 | 城市(编号，坐标) |
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| ------ | ----------------------------------------- |
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| 物品1 | [[0,[78, 34]], [1,[16, 56]] |
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| 物品2 | [[2,[98, 23]] |
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| 物品3 | [[3,[34, 15]], [4,[79, 46]], [5,[67,51]] |
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| 物品4 | [[6,[86, 13]], [7,[99, 46]] |
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| 物品5 | [[8,[47, 83]] |
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| 物品6 | [[ 9,[34, 55]], [10,[ 9, 21]] |
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| 物品7 | [[11,[45, 45]], [12,[100,34]] |
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| 物品8 | [[13,[88, 90]] |
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| 物品9 | [[14,[ 4, 51]] |
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| 物品10 | [[15,[73, 11]] |
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| 物品11 | [[16,[56, 37]] |
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##### 3.GTSP (24,15)
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| 物品 | 城市(编号，坐标) |
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| ------ | ----------------------------------------- |
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| 物品1 | [[0,[78, 34]], [1,[16, 56]] |
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| 物品2 | [[2,[98, 23]] |
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| 物品3 | [[3,[34, 15]], [4,[79, 46]], [5,[67,51]] |
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| 物品4 | [[6,[86, 13]], [7,[99, 46]] |
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| 物品5 | [[8,[47, 83]] |
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| 物品6 | [[ 9,[34, 55]], [10,[ 9, 21]] |
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| 物品7 | [[11,[45, 45]], [12,[100,34]] |
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| 物品8 | [[13,[88, 90]] |
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| 物品9 | [[14,[ 4, 51]] |
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| 物品10 | [[15,[73, 11]],[16,[26, 27]] |
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| 物品11 | [[17,[56, 37]] |
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| 物品12 | [[18,[100,13]], [19,[101,20]] |
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| 物品13 | [[20,[90, 87]], [21,[90, 87]] |
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| 物品14 | [[22,[ 1, 1]] |
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| 物品15 | [[23,[71, 33]] |
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##### 4.GTSP (31,16)
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| 物品 | 城市(编号，坐标) |
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| ------ | ----------------------------------------- |
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| 物品1 | [[0,[78, 34]], [1,[16, 56]] |
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| 物品2 | [[2,[98, 23]] |
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| 物品3 | [[3,[34, 15]], [4,[79, 46]], [5,[67,51]] |
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| 物品4 | [[6,[86, 13]], [7,[99, 46]] |
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| 物品5 | [[8,[47, 83]] |
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| 物品6 | [[ 9,[34, 55]], [10,[ 9, 21]] |
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| 物品7 | [[11,[45, 45]], [12,[100,34]] |
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| 物品8 | [[13,[88, 90]] |
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| 物品9 | [[14,[ 4, 51]], [15,[18, 52]] |
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| 物品10 | [[16,[73, 11]], [17,[26, 27]] |
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| 物品11 | [[18,[56, 37]], [19,[27, 70]], [20,[16, 16]] |
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| 物品12 | [[21,[100,13]], [22,[101,20]] |
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| 物品13 | [[23,[90, 87]], [24,[90, 87]] |
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| 物品14 | [[25,[10, 10]], [26,[ 1, 1]] |
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| 物品15 | [[27,[7, 13]], [28,[17, 23]], [29,[71, 33]] |
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| 物品16 | [30,[100,25]] |
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##### 5.GTSP(39,25)
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| 物品 | 城市(编号，坐标) |
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| ------ | ----------------------------------------- |
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|物品1| [[ 0,[78, 34]], [ 1,[16, 56]] |
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|物品2 |[[ 2,[98, 23]] |
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|物品3 |[[ 3,[34, 15]], [ 4,[79, 46]], [ 5,[67,51]] |
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|物品4 |[[ 6,[86, 13]], [ 7,[99, 46]] |
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|物品5 |[[ 8,[47, 83]], |
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|物品6 |[[ 9,[34, 55]], [10,[ 9, 21]], |
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|物品7 |[[11,[45, 45]], [12,[100,34]], |
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|物品8 |[[13,[88, 90]], |
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|物品9 |[[14,[ 4, 51]], [15,[18, 52]], |
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|物品10 |[[16,[73, 11]], [17,[26, 27]], |
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|物品11 |[[18,[56, 37]], [19,[27, 70]], |
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|物品12 |[[20,[100,13]], [21,[120,20]], |
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|物品13 |[[22,[90, 87]], [23,[90, 87]], |
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|物品14 |[[24,[10, 10]], |
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|物品15 |[[25,[7, 13]], |
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|物品16 |[[26,[ 90,75]], |
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|物品17 |[[27,[ 10,99]], |
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|物品18 |[[28,[103,105]], |
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|物品19 |[[29,[ 61,61]], [30,[ 51,51]], |
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|物品20 |[[31,[100, 5]], |
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|物品21 |[[32,[ 50,25]], |
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|物品22 |[[33,[ 50,50]], |
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|物品23 |[[34,[ 10,20]], |
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|物品24 |[[35,[ 31,20]], [36,[30,26]], [37,[34,35]] |
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|物品25 |[[38,[ 48,25]], |

‎README.md

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# :vertical_traffic_light: 启发式算法解决广义旅行商问题
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:vertical_traffic_light: 启发式算法解决广义旅行商问题
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#### 简介
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使用 <u>模拟退火</u>、<u>禁忌搜索</u>、<u>遗传算法</u>和<u>蚁群算法</u>共四种启发式算法来解决**广义旅行商问题**
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#### 问题实例
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[问题实例链接](./GTSP_instance.md)
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- GTSP(9,5) GTSP(17,11) GTSP(24,15) GTSP(31,16) GTSP(39,25)
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#### 算法流程
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![流程图](./images/process_total.jpg)
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#### 结果分析
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##### 复杂度
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> 针对五种GTSP实例，分别迭代100000次，计算其运行时间
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| 时间\s | 遗传算法 | 蚁群算法 | 模拟退火 | 禁忌搜索 |
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| ---- | -------- | -------- | -------- | -------- |
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|**GTSP(9,5)**| 215.1 | 1135.8 | 23.75 | 41.35 |
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|**GTSP(17,11)**| 291.5 | 4629.4 | 25.61 | 336.3 |
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|**GTSP(24,15)**| 416.3 | 8874.4 | 37.50 | 510.8 |
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|**GTSP(31,16)**| 522.7 | 11344.5 | 40.08 | 730.5 |
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|**GTSP(39,25)**| 617.2 | 15768.9 | 57.90 | 1624.0 |
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|平均 | 412.56 | 8,350.6 | 36.97 | 648.58 |
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##### 收敛性
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> 针对五种GTSP实例，分别迭代100000次，查看其每次迭代解的路径总距离
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###### GTSP(9,5)
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![](./images/iteration_9_5.jpg)
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###### GTSP(17,11)
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![](./images/iteration_17_11.jpg)
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###### GTSP(24,15)
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![](./images/iteration_24_15.jpg)
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###### GTSP(31,16)
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![](./images/iteration_31_16.jpg)
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###### GTSP(39,25)
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![](./images/iteration_39_25.jpg)
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##### 解比较
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> 针对五种GTSP实例，分别迭代100000次，查看最后解的效果
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###### GTSP(9,5)
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![](./images/solution_9_5.jpg)
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###### GTSP(17,11)
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![](./images/solution_17_11.jpg)
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###### GTSP(24,15)
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![](./images/solution_24_15.jpg)
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###### GTSP(31,16)
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![](./images/solution_31_16.jpg)
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###### GTSP(39,25)
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![](./images/solution_39_25.jpg)

‎algorithms/AntColonyAlgorithm.py

+37-19
Original file line numberDiff line numberDiff line change
@@ -43,13 +43,10 @@ def _remove_same_group_city(self,citys,choose):
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for group in self.TSP.city_index_groups:
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if choose in group:
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for city in group:
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try:
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citys.remove(city)
48-
except Exception as e:
49-
print(city,citys,group)
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raise e
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citys.remove(city)
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return citys
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def solve(self, record_step=100):
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''' 执行蚁群算法'''
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pheromone_mat=np.ones((citys_num,citys_num)) # 信息素浓度矩阵 初始为1
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path_mat=np.zeros((self.ants_num,items_num)).astype(int) # 路径矩阵
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# 选择初始点
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#!注意只适合有一个物品只有一个城市有的情况
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begin=random.choice([x[0] for x in self.TSP.city_index_groups if len(x)==1])
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star_t=time.time()
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print("======================[ AC ]===========================")
@@ -71,7 +74,9 @@ def solve(self, record_step=100):
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#1.=== 随机放置蚂蚁 并让所有蚂蚁爬行完毕 ====
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for ant in range(self.ants_num):
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unvisit_list=list(range(citys_num)) # 未访问的
74-
choose=random.choice(unvisit_list) # 初始随机的放置蚂蚁
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# choose=random.choice(unvisit_list) # 版本一 初始随机的放置蚂蚁
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choose=begin # 版本二 选择固定的起点
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unvisit_list=self._remove_same_group_city(unvisit_list,choose) # 移除有同类物品的城市
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# 记录开始城市
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for j in range(1,items_num):
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#轮盘法选择下一个城市
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trans_list,trans=[],0
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for k in range(len(unvisit_list)):
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for k in unvisit_list:
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# 计算概率 与信息素浓度成正比, 与距离成反比
85-
trans +=np.power(pheromone_mat[choose][unvisit_list[k]],self.alpha)*np.power(1.0/distMat[choose][k],self.beta)
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# print(pheromone_mat[choose][k],np.max(distMat[choose])/distMat[choose][k])
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trans +=np.power(pheromone_mat[choose][k],self.alpha)*np.power(np.max(distMat[choose])/distMat[choose][k],self.beta)
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trans_list.append(trans)
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# print(trans_list)
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rand=random.uniform(0,trans)#产生随机数
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# 转一次轮盘 选择
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#所有蚂蚁的路径表填满之后，算每只蚂蚁的总距离
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dis_all_ant_list=self.cal_path_distance(path_mat)
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min_distance=min(dis_all_ant_list)
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min_path=path_mat[dis_all_ant_list.index(min_distance)].copy()
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#3.=========== 更新信息素矩阵 ==============
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pheromone_change=np.zeros((citys_num,citys_num))
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for i in range(self.ants_num):
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# 在路径上的每两个相邻城市间留下信息素，与路径距离反比
111-
for j in range(items_num-1):
112-
pheromone_change[path_mat[i,j]][path_mat[i,j+1]] += self.Q/distMat[path_mat[i,j]][path_mat[i,j+1]]
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pheromone_change[path_mat[i,items_num-1]][path_mat[i,0]] += self.Q/distMat[path_mat[i,items_num-1]][path_mat[i,0]]
114-
pheromone_mat=(1-self.Rho)*pheromone_mat+pheromone_change
118+
# 版本一 所有的都会增加
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# for i in range(self.ants_num):
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# # 在路径上的每两个相邻城市间留下信息素，与路径距离反比
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# for j in range(items_num-1):
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# pheromone_change[path_mat[i,j]][path_mat[i,j+1]] += self.Q*(np.max(distMat[path_mat[i,j]])/distMat[path_mat[i,j]][path_mat[i,j+1]])
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# pheromone_change[path_mat[i,items_num-1]][path_mat[i,0]] += self.Q*(np.max(distMat[path_mat[i,items_num-1]])/distMat[path_mat[i,items_num-1]][path_mat[i,0]])
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# pheromone_mat=(1-self.Rho)*pheromone_mat+pheromone_change
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# # 版本二 只有最优路径的信息素才会增加
127+
if count == 0 or min_distance < dis_new:
128+
for i in range(0,len(min_path)-1):
129+
pheromone_change[min_path[i]][min_path[i+1]]+=self.Q
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pheromone_change[min_path[i+1]][min_path[0]]+=self.Q
131+
pheromone_mat=(1-self.Rho)*pheromone_mat+pheromone_change
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116135
#记录历史最佳值
117-
if count == 0 or min(dis_all_ant_list) < dis_new:
118-
dis_new=min(dis_all_ant_list)
119-
path_new=path_mat[dis_all_ant_list.index(dis_new)].copy()
136+
if count == 0 or min_distance < dis_new:
137+
dis_new,path_new=min_distance,min_path
120138
self.TSP.set_path(path_new)
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122140
# 记录迭代的值
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128146
end_t=time.time()
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print("=============[ path:{} cost:{} time:{:.4}s]===============".format(self.TSP.path,self.TSP.distance,end_t-star_t))
148+
print("=============[ path:{} cost:{} time:{:.5}s]===============".format(self.TSP.path,self.TSP.distance,end_t-star_t))
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return self.TSP
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‎algorithms/GeneticAlgorithm.py

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Original file line numberDiff line numberDiff line change
@@ -86,8 +86,12 @@ def cross(self,pops):
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# 必须产生新的
8787
p,q=random.randint(0,len(self.TSP.city_index_groups)-1),random.randint(0,len(self.TSP.city_index_groups)-1)
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pop[p],pop[q]=pop[q],pop[p] # 第一次交叉
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m,n=random.randint(0,len(self.TSP.city_index_groups)-1),random.randint(0,len(self.TSP.city_index_groups)-1)
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pop[m],pop[n]=pop[n],pop[m] # 第二次交叉
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# m,n=random.randint(0,len(self.TSP.city_index_groups)-1),random.randint(0,len(self.TSP.city_index_groups)-1)
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# pop[m],pop[n]=pop[n],pop[m] # 第二次交叉
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# pop[m],pop[n]=pop[n],pop[m] # 第三次交叉
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# m,n=random.randint(0,len(self.TSP.city_index_groups)-1),random.randint(0,len(self.TSP.city_index_groups)-1)
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# pop[m],pop[n]=pop[n],pop[m] # 第四次交叉
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new_pops.append(pop)
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return new_pops
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‎algorithms/TabuSearch.py

+7-4
Original file line numberDiff line numberDiff line change
@@ -36,8 +36,10 @@ def find_new_path(self,best_path):
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paths=[]
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# 1. 第一类 交换城市顺序
39-
for i in range(1,len(best_path)-1):
39+
for i in range(1,len(best_path)):
4040
for j in range(i+1,len(best_path)):
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# j=i
42+
# while j==i: j=random.choice(list(range(len(best_path))))
4143
path=best_path.copy()
4244
path[i],path[j]=path[j],path[i]
4345
paths.append(path)
@@ -46,8 +48,9 @@ def find_new_path(self,best_path):
4648
for i in range(len(best_path)):
4749
for group in self.TSP.city_index_groups:
4850
if best_path[i] in group:
49-
group.remove(best_path[i]) # 移除自己
50-
for other_city in group:
51+
group_copy=group.copy()
52+
group_copy.remove(best_path[i]) # 移除自己
53+
for other_city in group_copy:
5154
path=best_path.copy()
5255
path[i]=other_city
5356
paths.append(path)
@@ -93,7 +96,7 @@ def solve(self, record_step=100):
9396
elif best_path in self.taboo_table:
9497
#2.2===大于期望 且最优解在禁忌表===
9598
# 选择不在禁忌表中的最优解
96-
while best_path in self.taboo_table:
99+
while best_path in self.taboo_table :
97100
paths.remove(best_path)
98101
best_dist,best_path=self.find_best_dist_path(paths)
99102

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