以下是使用模拟退火算法解决tsp问题的python代码示例:
在代码中,我们定义了distance()函数来计算两个城市之间的欧氏距离,定义了path_length()函数来计算一条路径的总长度,定义了initial_solution()函数来随机生成一个初始解。利用这些函数,我们定义了模拟退火算法的主函数simulated_annealing()。在该函数中,我们迭代过程中根据当前温度随机生成新解,并根据模拟退火算法判断是否选择该新解。我们还定义acceptance_probability()函数来计算新解的被接受的概率。最终,我们在测试程序中输入了城市坐标,并使用模拟退火算法求解tsp问题,输出了最优路径和最优路径长度。
这是一个简单的示例,实际应用过程中需要考虑更多的问题,如调整参数、增加限制条件等。
import math
import random
# 计算两点间的欧氏距离
def distance(p1, p2):
return math.sqrt((p1[0]-p2[0])**2 + (p1[1]-p2[1])**2)
# 计算一条路径的总长度
def path_length(path, cities):
total = 0
for i in range(len(path)):
total += distance(cities[path[i]], cities[path[(i+1)%len(path)]])
return total
# 随机生成一个初始解
def initial_solution(cities):
path = list(range(len(cities)))
random.shuffle(path)
return path
# 模拟退火算法
def simulated_annealing(cities, T = 1.0, alpha = 0.95, stopping_T = 0.0001, stopping_iter = 1000):
# 随机生成初始解
curr_solution = initial_solution(cities)
best_solution = curr_solution[:]
# 计算初始解的路径长度
curr_length = path_length(curr_solution, cities)
best_length = curr_length
# 记录迭代次数
iter_count = 0
# 迭代过程中不断降温
while T > stopping_T and iter_count < stopping_iter:
# 随机生成新解
i, j = sorted(random.sample(range(len(cities)), 2))
new_solution = curr_solution[:i] + curr_solution[j:j+1] + curr_solution[i+1:j] + curr_solution[i:i+1] + curr_solution[j+1:]
# 计算新解的路径长度
new_length = path_length(new_solution, cities)
# 模拟退火过程
ap = acceptance_probability(curr_length, new_length, T)
if ap > random.random():
curr_solution = new_solution
curr_length = new_length
# 记录最优解
if curr_length < best_length:
best_solution = curr_solution[:]
best_length = curr_length
# 不断降温
T *= alpha
iter_count += 1
return best_solution, best_length
# 计算新解的被接受的概率
def acceptance_probability(curr_length, new_length, temperature):
if new_length < curr_length:
return 1.0
else:
return math.exp((curr_length - new_length) / temperature)
# 测试程序
if __name__ == "__main__":
# 输入城市坐标
cities = []
cities.append((200, 50))
cities.append((150, 150))
cities.append((50, 100))
cities.append((100, 200))
cities.append((200, 200))
# 使用模拟退火算法求解tsp问题
best_solution, best_length = simulated_annealing(cities)
print("最优路径:", best_solution)
print("最优路径长度:", best_length)
版权声明:本文为wzj05467原创文章,遵循 CC 4.0 BY-SA 版权协议,转载请附上原文出处链接和本声明。