模拟退火算法python源码

模拟退火算法是一种用于求解全局优化问题的随机搜索算法，它模拟了金属冷却过程中的晶格结构变化。以下是基于Python的一个简化版的模拟退火算法实现：

import random

def initial_solution(n):
    # 生成初始解决方案
    return [random.randint(0, 1) for _ in range(n)]

def energy(solution):
    # 计算当前解决方案的能量函数值
    # 这里假设是一个简单的平方和形式
    return sum(solution[i] * solution[(i + 1) % n] for i in range(n))

def neighbor(solution):
    # 随机生成邻域状态
    new_solution = solution.copy()
    i = random.randint(0, len(new_solution) - 1)
    if random.random() < 0.5:
        new_solution[i] = 1 - new_solution[i]
    return new_solution

def simulated_annealing(T, T_min, max_steps, solution):
    current_energy = energy(solution)
    best_energy = current_energy
    best_solution = solution

    steps = 0
    while T > T_min and steps < max_steps:
        new_solution = neighbor(solution)
        new_energy = energy(new_solution)

        delta_E = new_energy - current_energy
        if delta_E < 0 or random.random() < exp(-delta_E / T):
            current_energy = new_energy
            solution = new_solution

        if new_energy < best_energy:
            best_energy = new_energy
            best_solution = solution

        T *= 0.99  # 温度随步骤减小
        steps += 1

    return best_solution, best_energy

# 示例用法
n = 10  # 解决问题的维度
solution = initial_solution(n)
T = 1000  # 初始温度
T_min = 0.01  # 最终温度
max_steps = 1000  # 总步数
best_solution, best_energy = simulated_annealing(T, T_min, max_steps, solution)
print(f"Best solution: {best_solution}, Energy: {best_energy}")