python中如何实现模拟退火算法,请举个例子
时间: 2024-09-21 20:12:25 浏览: 30
在Python中,模拟退火算法是一种优化问题求解策略,通常用于解决复杂函数的全局最小化问题。它基于金属冷却过程中的相变原理,通过随机接受能量较高的状态来跳出局部最优,逐渐接近全局最优解。以下是使用Python实现一个简单模拟退火算法的一个基本步骤:
```python
import random
def energy(state): # 定义目标函数或评价函数
return state ** 2 # 这里只是一个简单的示例,实际应用可能会更复杂
def accept_prob(current_state, new_state, temp):
current_energy = energy(current_state)
new_energy = energy(new_state)
delta_e = new_energy - current_energy
if delta_e <= 0 or random.random() < math.exp(-delta_e / temp):
return True
else:
return False
def simulated_annealing(starting_state, end_temp, cooling_rate, num_iterations):
current_state = starting_state
temperature = end_temp
for _ in range(num_iterations):
new_state = perturb(current_state) # 拟合问题的改变操作
if accept_prob(current_state, new_state, temperature):
current_state = new_state
temperature *= cooling_rate
return current_state, energy(current_state)
# 示例,寻找一维平面上最小值
starting_state = [5]
end_temp = 1000
cooling_rate = 0.99
num_iterations = 1000
solution, min_energy = simulated_annealing(starting_state, end_temp, cooling_rate, num_iterations)
print(f"Solution: {solution}, Minimum Energy: {min_energy}")