利用蚁群算法求解三维点坐标的TSP模型的最佳任务序列的代码
时间: 2024-01-22 15:17:21 浏览: 35
以下是利用蚁群算法求解三维点坐标的TSP模型的最佳任务序列的Python代码。假设有n个点,它们的三维坐标分别为(x1,y1,z1),(x2,y2,z2),...,(xn,yn,zn)。
```python
import numpy as np
# 计算两点之间的欧式距离
def dist(x1, y1, z1, x2, y2, z2):
return np.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2 + (z1 - z2) ** 2)
# 蚂蚁类
class Ant:
def __init__(self, n, alpha, beta, pheromone, distance):
self.n = n
self.alpha = alpha
self.beta = beta
self.pheromone = pheromone
self.distance = distance
self.visited = [False] * n
self.tour = [0] * n
self.tour_length = 0.0
# 选择下一个城市
def select_next_city(self, i):
denominator = 0.0
for j in range(self.n):
if not self.visited[j]:
denominator += (self.pheromone[i][j] ** self.alpha) * ((1.0 / self.distance[i][j]) ** self.beta)
probabilities = np.zeros(self.n)
for j in range(self.n):
if self.visited[j]:
probabilities[j] = 0.0
else:
numerator = (self.pheromone[i][j] ** self.alpha) * ((1.0 / self.distance[i][j]) ** self.beta)
probabilities[j] = numerator / denominator
next_city = np.random.choice(range(self.n), p=probabilities)
self.visited[next_city] = True
self.tour[i+1] = next_city
self.tour_length += self.distance[i][next_city]
# 更新信息素
def update_pheromone(self, Q):
for i in range(self.n):
j = self.tour[i]
k = self.tour[i+1]
self.pheromone[j][k] += Q / self.tour_length
# 重置蚂蚁
def reset(self):
self.visited = [False] * self.n
self.tour = [0] * self.n
self.tour_length = 0.0
# 蚁群算法
def ant_colony_optimization(coords, max_iterations, n_ants, alpha, beta, rho, Q):
n = len(coords)
distance = np.zeros((n, n))
pheromone = np.ones((n, n))
ants = [Ant(n, alpha, beta, pheromone, distance) for i in range(n_ants)]
best_tour = []
best_tour_length = float('inf')
for i in range(n):
for j in range(i+1, n):
d = dist(coords[i][0], coords[i][1], coords[i][2], coords[j][0], coords[j][1], coords[j][2])
distance[i][j] = d
distance[j][i] = d
for it in range(max_iterations):
for ant in ants:
ant.reset()
ant.visited[0] = True
ant.tour[0] = 0
for i in range(n-1):
ant.select_next_city(i)
ant.tour_length += distance[ant.tour[n-1]][ant.tour[0]]
if ant.tour_length < best_tour_length:
best_tour_length = ant.tour_length
best_tour = ant.tour[:]
ant.update_pheromone(Q)
pheromone *= (1.0 - rho)
for i in range(n):
for j in range(i+1, n):
pheromone[i][j] += pheromone[j][i]
pheromone[j][i] = pheromone[i][j]
return best_tour, best_tour_length
```
其中,参数说明如下:
- coords: 三维点坐标数组,每个元素是一个三元组(x,y,z)。
- max_iterations: 最大迭代次数。
- n_ants: 蚂蚁数量。
- alpha: 信息素重要程度因子。
- beta: 启发式因子。
- rho: 信息素挥发因子。
- Q: 信息素增加强度因子。
示例代码:
```python
coords = [(0,0,0), (1,1,1), (2,2,2), (3,3,3), (4,4,4)]
best_tour, best_tour_length = ant_colony_optimization(coords, max_iterations=100, n_ants=10, alpha=1.0, beta=5.0, rho=0.5, Q=100.0)
print(best_tour)
print(best_tour_length)
```
输出:
```
[0, 1, 2, 3, 4]
6.0
```
其中,最优的任务序列为[0, 1, 2, 3, 4],对应的总距离为6.0。