模拟退火 python r102
时间: 2023-06-21 22:09:52 浏览: 54
模拟退火算法(Simulated Annealing,SA)是一种通用的优化算法,它模拟物质从高温到低温的退火过程,通过不断降低温度,使得系统达到最优状态。
下面是一个简单的 Python 实现:
```python
import math
import random
def simulated_annealing(cost_function, initial_state, initial_temperature, cooling_rate, min_temperature):
current_state = initial_state
current_cost = cost_function(current_state)
temperature = initial_temperature
while temperature > min_temperature:
neighbor_state = get_neighbor(current_state)
neighbor_cost = cost_function(neighbor_state)
delta = neighbor_cost - current_cost
if delta < 0:
current_state = neighbor_state
current_cost = neighbor_cost
else:
probability = math.exp(-delta / temperature)
if random.random() < probability:
current_state = neighbor_state
current_cost = neighbor_cost
temperature *= cooling_rate
return current_state, current_cost
def get_neighbor(state):
# 生成一个随机的邻居状态
pass
def cost_function(state):
# 计算状态的代价
pass
# 示例
initial_state = ...
initial_temperature = ...
cooling_rate = ...
min_temperature = ...
best_state, best_cost = simulated_annealing(cost_function, initial_state, initial_temperature, cooling_rate, min_temperature)
print("Best state:", best_state)
print("Best cost:", best_cost)
```
其中,`cost_function` 是代价函数,`initial_state` 是初始状态,`initial_temperature` 是初始温度,`cooling_rate` 是降温速率,`min_temperature` 是最小温度。
在 `simulated_annealing` 函数中,首先初始化当前状态和代价,然后不断迭代直到达到最小温度。每次迭代,先生成一个随机的邻居状态,然后计算邻居状态的代价与当前状态的代价之差。如果邻居状态的代价比当前状态的代价更优,则接受邻居状态;否则以一定的概率接受邻居状态,概率随温度的降低而减小。最终返回最优状态和最优代价。
在实际应用中,需要根据具体问题来定义代价函数和邻居状态的生成方式。同时,需要设置合适的初始温度、降温速率和最小温度,以保证算法能够在合理的时间内收敛到最优解。