模拟退火算法python

模拟退火算法（Simulated Annealing，SA）是一种通用概率演算法，用来在一个大的搜寻空间内找寻函数的最优解。下面是一个简单的Python实现：

import math
import random

# 目标函数
def objective_function(x):
    return math.sin(10*x) * x + math.cos(2*x) * x

# 状态转移函数：随机生成下一个状态
def get_neighbor(x, step=0.1):
    return x + random.uniform(-step, step)

# 计算概率
def acceptance_probability(cost, new_cost, temperature):
    if new_cost < cost:
        return 1.0
    else:
        return math.exp((cost - new_cost) / temperature)

# 模拟退火算法
def simulated_annealing(initial_solution, objective_function, get_neighbor, acceptance_probability, temperature=10000, cooling_rate=0.95, stopping_temperature=1e-8):
    current_solution = initial_solution
    current_cost = objective_function(current_solution)
    best_solution = current_solution
    best_cost = current_cost
    
    while temperature > stopping_temperature:
        for i in range(100):
            new_solution = get_neighbor(current_solution)
            new_cost = objective_function(new_solution)
            ap = acceptance_probability(current_cost, new_cost, temperature)
            if ap > random.random():
                current_solution = new_solution
                current_cost = new_cost
                if current_cost < best_cost:
                    best_solution = current_solution
                    best_cost = current_cost
        temperature *= cooling_rate
        
    return best_solution, best_cost

# 测试
initial_solution = random.uniform(-10, 10)
best_solution, best_cost = simulated_annealing(initial_solution, objective_function, get_neighbor, acceptance_probability)

print("Best solution: {:.4f}".format(best_solution))
print("Best cost: {:.4f}".format(best_cost))

在以上代码中，`objective_function`是目标函数，`get_neighbor`是状态转移函数，`acceptance_probability`用于计算接受新解的概率。在`simulated_annealing`函数中，我们通过不断降温来寻找最优解。最后，我们输出最优解和最优解的目标函数值。