模拟退火算法代码实现

模拟退火算法是一种全局优化搜索技术，常用于解决复杂函数的最小化问题。其基本思想是从初始解开始，通过一定的概率接受当前状态的“坏”解，以增加算法跳出局部最优的可能性。以下是模拟退火算法的一个简单Python代码实现：

import random

def acceptance_probability(current_state, new_state, temperature):
    delta_energy = energy(new_state) - energy(current_state)
    return min(1, np.exp(-delta_energy / temperature))

def simulate_annealing(starting_state, target_function, initial_temperature, cooling_rate, num_iterations):
    current_state = starting_state
    best_state = starting_state
    best_energy = target_function(starting_state)

    for _ in range(num_iterations):
        new_state = perturb(current_state)
        probability = acceptance_probability(current_state, new_state, temperature)

        if probability > random.random() or target_function(new_state) < best_energy:
            current_state = new_state
            if target_function(new_state) < best_energy:
                best_state = new_state
                best_energy = target_function(new_state)

        temperature *= cooling_rate

    return best_state

# 假设energy是一个计算目标函数值的函数，perturb生成一个新的状态
starting_state = ... # 初始化状态
target_function = ...
initial_temperature = ...
cooling_rate = ...
num_iterations = ...

best_solution = simulate_annealing(starting_state, target_function, initial_temperature, cooling_rate, num_iterations)

在这个代码里，`energy`函数是用来计算状态能量的，`perturb`函数则是对当前状态做微小随机扰动生成新状态。在每一步迭代中，都会根据接受概率决定是否接受新状态。