还有一些别的变领域搜索算法的邻域函数吗
时间: 2023-11-18 18:06:23 浏览: 36
是的,还有其他一些邻域函数,例如随机邻域函数、模拟退火邻域函数、遗传算法邻域函数等等。随机邻域函数是指在当前解的邻域中随机选择一个解作为下一次迭代的解;模拟退火邻域函数是指根据一定的概率接受劣解,并且随着迭代次数的增加,概率逐渐减小;遗传算法邻域函数是指通过交叉、变异等操作生成新的解,并选择其中最好的解作为下一次迭代的解。这些邻域函数都可以应用于不同的问题,并且有一定的优缺点。
相关问题
变邻域搜索算法python
变邻域搜索(VNS)是一种基于局部搜索的启发式优化算法,它通过在不同的邻域内搜索来寻找最优解。以下是一个简单的变邻域搜索算法的 Python 实现:
```python
import random
def vns(solution, neighborhoods, max_iter):
"""
solution: 初始解
neighborhoods: 邻域生成函数列表
max_iter: 最大迭代次数
return: 最优解
"""
best_solution = solution
k = 1
while k <= max_iter:
for neighborhood in neighborhoods:
candidate = neighborhood(best_solution)
if candidate < best_solution:
best_solution = candidate
k = 1
break
else:
k += 1
return best_solution
```
在这个实现中,我们将初始解作为当前的最优解,然后在每个邻域内搜索,如果找到更优的解,则更新当前的最优解。如果在某个邻域内达到了 `max_iter` 次未找到更优的解,则递增 `k` 值,进入下一个邻域的搜索。如果找到了更优的解,则将 `k` 重置为 1,重新从第一个邻域开始搜索。
在使用这个算法时,我们需要定义一个或多个邻域生成函数。邻域生成函数将当前解作为输入,返回一个新的解。例如,以下是一个简单的邻域生成函数,它随机交换解中的两个元素:
```python
def swap_neighborhood(solution):
"""
随机交换解中的两个元素
"""
n = len(solution)
i, j = random.randint(0, n-1), random.randint(0, n-1)
new_solution = solution.copy()
new_solution[i], new_solution[j] = new_solution[j], new_solution[i]
return new_solution
```
我们可以将邻域生成函数组合成一个列表,然后传递给 `vns` 函数。例如,以下代码将使用上面的 `swap_neighborhood` 函数和另一个邻域生成函数来运行 VNS 算法:
```python
neighborhoods = [swap_neighborhood, reverse_neighborhood]
best_solution = vns(initial_solution, neighborhoods, max_iter)
```
变邻域搜索算法求解置换flow shop的python代码
以下是使用变邻域搜索算法求解置换flow shop问题的Python代码:
```python
import random
def calculate_cmax(permutation, processing_times):
n = len(processing_times[0])
m = len(processing_times)
cmax = [0] * n
for j in range(n):
if j == 0:
cmax[0] = processing_times[permutation[0]][0]
else:
cmax[j] = cmax[j-1] + processing_times[permutation[0]][j]
for i in range(1, m):
if j == 0:
cmax[j] += processing_times[permutation[i]][j]
else:
cmax[j] = max(cmax[j], cmax[j-1]) + processing_times[permutation[i]][j]
return cmax[-1]
def generate_initial_solution(n):
return list(range(n))
def swap(permutation, i, j):
permutation[i], permutation[j] = permutation[j], permutation[i]
def neighborhood_1(permutation):
neighborhood = []
for i in range(len(permutation)):
for j in range(i+1, len(permutation)):
neighbor = list(permutation)
swap(neighbor, i, j)
neighborhood.append(neighbor)
return neighborhood
def neighborhood_2(permutation):
neighborhood = []
for i in range(len(permutation)):
for j in range(i+2, len(permutation)):
neighbor = list(permutation)
neighbor[i+1:j+1] = reversed(neighbor[i+1:j+1])
neighborhood.append(neighbor)
return neighborhood
def variable_neighborhood_search(processing_times, max_iterations):
current_solution = generate_initial_solution(len(processing_times))
best_solution = list(current_solution)
for i in range(max_iterations):
neighborhood = neighborhood_1(current_solution) + neighborhood_2(current_solution)
random.shuffle(neighborhood)
for neighbor in neighborhood:
if calculate_cmax(neighbor, processing_times) < calculate_cmax(current_solution, processing_times):
current_solution = list(neighbor)
if calculate_cmax(current_solution, processing_times) < calculate_cmax(best_solution, processing_times):
best_solution = list(current_solution)
break
return best_solution
# Example usage
processing_times = [[2, 7, 3], [9, 2, 8], [6, 4, 5]]
solution = variable_neighborhood_search(processing_times, 1000)
print("Best solution:", solution)
print("Cmax:", calculate_cmax(solution, processing_times))
```
在此示例中,`processing_times` 是一个 $m \times n$ 的二维列表,其中 $m$ 是作业数,$n$ 是机器数,表示每个作业在每个机器上的加工时间。`variable_neighborhood_search` 函数接受 `processing_times` 和 `max_iterations` 两个参数,返回一个包含最佳解的置换。`calculate_cmax` 函数接受一个置换和 `processing_times`,返回在该置换下的最大完工时间 `Cmax`。`generate_initial_solution` 函数返回一个初始解,`swap` 函数交换置换中两个元素的位置,`neighborhood_1` 和 `neighborhood_2` 分别生成大小为 $n(n-1)/2$ 和 $n(n-3)/2$ 的两个邻域。最后,我们使用 `processing_times` 和 `solution` 调用 `calculate_cmax` 函数来计算最佳解的 `Cmax`。