在上述代码基础上绘制最优路径图
时间: 2024-03-23 21:36:42 浏览: 57
以下是在上述代码基础上绘制最优路径图的示例代码:
```python
import random
import math
import matplotlib.pyplot as plt
# 34个省会城市的坐标
cities = [
(1150, 1760), (630, 1660), (40, 2090), (750, 1100),
(750, 2030), (1030, 2070), (1650, 650), (1490, 1630),
(790, 2260), (710, 1310), (840, 550), (1170, 2300),
(970, 1340), (510, 700), (750, 900), (1280, 1200),
(230, 590), (460, 860), (1040, 950), (590, 1390),
(830, 1770), (490, 500), (1840, 1240), (1260, 1500),
(1280, 790), (490, 2130), (1460, 1420), (1260, 1910),
(360, 1980), (230, 1100), (1310, 1000), (550, 1200),
(590, 1950), (830, 1360)
]
# 计算两个城市之间的距离
def distance(city1, city2):
return math.sqrt((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2)
# 计算路径的总长度
def total_distance(path):
return sum(distance(cities[path[i]], cities[path[i + 1]]) for i in range(len(path) - 1)) + distance(cities[path[0]], cities[path[-1]])
# 模拟退火算法
def simulated_annealing(T=10000, Tmin=1e-8, alpha=0.99):
# 随机初始化路径
path = list(range(len(cities)))
random.shuffle(path)
# 计算初始路径长度
energy = total_distance(path)
# 记录最优解
best_path = path
best_energy = energy
# 降温过程
while T > Tmin:
# 随机交换两个城市的位置
i, j = random.sample(range(len(cities)), 2)
new_path = path[:]
new_path[i], new_path[j] = new_path[j], new_path[i]
# 计算新路径长度
new_energy = total_distance(new_path)
# 计算能量差
delta = new_energy - energy
# 如果新路径更优,则接受新路径
if delta < 0 or math.exp(-delta / T) > random.random():
path = new_path
energy = new_energy
# 更新最优解
if energy < best_energy:
best_path = path
best_energy = energy
# 降温
T *= alpha
return best_path, best_energy
# 绘制最优路径图
best_path, best_energy = simulated_annealing()
x = [cities[i][0] for i in best_path] + [cities[best_path[0]][0]]
y = [cities[i][1] for i in best_path] + [cities[best_path[0]][1]]
plt.plot(x, y, marker='o')
plt.show()
```
该代码使用matplotlib库绘制了最优路径图,其中x和y分别表示最优路径上城市的横纵坐标,最后一个点为起点,marker为圆形。运行该代码可以得到最优路径图,可以直观地看到最短路径经过了哪些城市。
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