动态规划tsp旅行商问题Python
时间: 2023-09-15 20:23:03 浏览: 78
旅行商问题是一个经典的组合优化问题,它的目标是找到一条路径,使得一个旅行商能够访问一组城市,同时最小化总距离或总成本。动态规划是解决旅行商问题的一种常见方法。下面是一个Python实现的动态规划TSP算法:
```python
import sys
from itertools import permutations
def tsp_dp(cities):
# 计算城市之间的距离矩阵
n = len(cities)
dist = [[0] * n for i in range(n)]
for i in range(n):
for j in range(n):
dist[i][j] = distance(cities[i], cities[j])
# 初始化动态规划表
dp = [[-1] * (1 << n) for i in range(n)]
for i in range(n):
dp[i][1 << i] = 0
# 动态规划
for mask in range(1, 1 << n):
for i in range(n):
if mask & (1 << i) == 0:
continue
for j in range(n):
if i == j or mask & (1 << j) == 0:
continue
prev_mask = mask ^ (1 << i)
if dp[i][mask] == -1:
continue
if dp[j][prev_mask] == -1:
dp[j][prev_mask] = dp[i][mask] + dist[i][j]
else:
dp[j][prev_mask] = min(dp[j][prev_mask], dp[i][mask] + dist[i][j])
# 找到最小旅行距离
min_dist = sys.maxsize
for i in range(n):
if dp[i][(1 << n) - 1] == -1:
continue
min_dist = min(min_dist, dp[i][(1 << n) - 1] + dist[i][0])
return min_dist
def distance(city1, city2):
return ((city1[0] - city2[0]) ** 2 + (city1[1] - city2[1]) ** 2) ** 0.5
# 示例
cities = [(0, 0), (1, 2), (3, 4), (5, 6)]
print(tsp_dp(cities))
```
该算法使用动态规划来计算从每个城市开始的最小旅行距离。它首先计算城市之间的距离矩阵,然后初始化一个动态规划表。每个单元格表示从一个城市出发,访问特定子集的城市的最小距离。然后,它使用一个循环来填充动态规划表,直到所有子集都被处理。最后,找到最小旅行距离并返回。