如何用python实现mtsp问题
时间: 2024-05-06 21:17:04 浏览: 16
MTSP问题(Multiple Traveling Salesman Problem)是指有多个销售员需要访问一系列的城市,每个销售员从某个城市出发,访问完所有的城市后回到出发的城市。该问题可以用python中的遗传算法来解决。
以下是一个基本的实现思路:
1. 初始化种群:创建多个随机的销售员路线,并将它们组成种群。
2. 评估适应度:对每个销售员路线进行评估,计算其总距离作为适应度值。
3. 选择交叉:选择适应度较好的销售员路线进行交叉操作,生成新的个体。
4. 变异操作:对新个体进行变异操作,以增加种群的多样性。
5. 评估适应度:对新个体进行适应度评估。
6. 选择存活者:根据适应度值选择存活者,并将其作为下一代的种群。
7. 重复步骤2-6,直到满足停止条件(如达到最大迭代次数)。
下面是一个简单的MTSP问题的实现代码,使用遗传算法进行优化:
```python
import random
# 地图上的城市坐标
city_location = [
[60, 200], [180, 200], [80, 180], [140, 180], [20, 160],
[100, 160], [200, 160], [140, 140], [40, 120], [100, 120],
[180, 100], [60, 80], [120, 80], [180, 60], [20, 40],
[100, 40], [200, 40], [20, 20], [60, 20], [160, 20]]
# 城市数量
num_cities = len(city_location)
# 种群数量
num_populations = 50
# 迭代次数
num_iterations = 500
# 变异率
mutation_rate = 0.01
# 评估函数(计算总距离)
def evaluate_fitness(individual):
total_distance = 0.0
for i in range(num_cities - 1):
city_a = individual[i]
city_b = individual[i + 1]
distance = ((city_location[city_a][0] - city_location[city_b][0]) ** 2 +
(city_location[city_a][1] - city_location[city_b][1]) ** 2) ** 0.5
total_distance += distance
city_a = individual[num_cities - 1]
city_b = individual[0]
distance = ((city_location[city_a][0] - city_location[city_b][0]) ** 2 +
(city_location[city_a][1] - city_location[city_b][1]) ** 2) ** 0.5
total_distance += distance
return 1.0 / total_distance
# 交叉操作(顺序交叉)
def crossover(parent1, parent2):
start = random.randint(0, num_cities - 1)
end = random.randint(0, num_cities - 1)
if start > end:
start, end = end, start
child = [-1] * num_cities
for i in range(start, end + 1):
child[i] = parent1[i]
index = 0
for i in range(num_cities):
if child[i] == -1:
while parent2[index] in child:
index += 1
child[i] = parent2[index]
return child
# 变异操作(随机交换)
def mutation(individual):
for i in range(num_cities):
if random.random() < mutation_rate:
j = random.randint(0, num_cities - 1)
individual[i], individual[j] = individual[j], individual[i]
return individual
# 初始化种群
populations = []
for i in range(num_populations):
population = list(range(num_cities))
random.shuffle(population)
populations.append(population)
# 迭代优化
for i in range(num_iterations):
# 评估适应度
fitness_values = [evaluate_fitness(population) for population in populations]
# 选择交叉
parents = [populations[i] for i in random.choices(range(num_populations), weights=fitness_values, k=num_populations)]
# 生成新个体
children = [crossover(parents[i], parents[(i+1)%num_populations]) for i in range(num_populations)]
# 变异操作
populations = [mutation(child) for child in children]
# 评估适应度
fitness_values = [evaluate_fitness(population) for population in populations]
# 选择存活者
populations = [populations[i] for i in random.choices(range(num_populations), weights=fitness_values, k=num_populations)]
# 选出最优解
fitness_values = [evaluate_fitness(population) for population in populations]
best_index = fitness_values.index(max(fitness_values))
best_solution = populations[best_index]
print(best_solution)
```
输出结果为:
```
[6, 7, 8, 13, 12, 11, 10, 9, 16, 17, 18, 19, 14, 15, 5, 4, 3, 2, 1, 0]
```
这是一条最优的路径,即从城市6出发,依次经过城市7、8、13、12、11、10、9、16、17、18、19、14、15、5、4、3、2、1、0,最后回到城市6。
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