模拟退火算法的python和matlab详细代码示例及适用范围

模拟退火算法是一种全局优化搜索技术，常用于解决复杂的组合优化问题，如旅行商问题、0-1背包问题等。以下是Python和MATLAB的简单模拟退火算法代码示例：

**Python代码示例：**

import random
import numpy as np

def acceptance_probability(T, E_new, E_old):
    return min(1, np.exp(-(E_new - E_old) / T))

def simulated_annealing(fitness_func, initial_state, temperature=1000, cooling_rate=0.95, max_steps=1000):
    current_state = initial_state
    best_state = current_state
    best_fitness = fitness_func(current_state)

    for _ in range(max_steps):
        new_state = make_random_neighbor(current_state)
        new_fitness = fitness_func(new_state)

        if new_fitness < best_fitness or random.random() < acceptance_probability(temperature, new_fitness, best_fitness):
            best_state = new_state
            best_fitness = new_fitness

        temperature *= cooling_rate
        if temperature < 1e-6:
            break

    return best_state, best_fitness

# 假设fitness_func是目标函数，make_random_neighbor是一个生成新状态的函数
best_solution, optimal_value = simulated_annealing(some_function, some_initial_state)

**MATLAB代码示例：**

function [best_solution, optimal_value] = simulatedAnnealing(initial_state, fitness_func, varargin)
% 初始化参数
T = varargin{1};
cooling_rate = varargin{2}(1);
max_steps = varargin{2}(2);

% 记录最佳解和最优值
best_state = initial_state;
best_fitness = fitness_func(best_state);

for step = 1:max_steps
    % 生成邻居状态
    new_state = generateRandomNeighbor(best_state);
    
    % 计算新的适应度
    new_fitness = fitness_func(new_state);
    
    % 接受或拒绝新状态
    if (new_fitness < best_fitness || ...
       rand() < exp(-(new_fitness - best_fitness) / T))
        best_state = new_state;
        best_fitness = new_fitness;
    end
    
    % 降低温度并检查收敛条件
    T = T * cooling_rate;
    if T < 1e-6
        break;
    end
end

% 返回结果
best_solution = best_state;
optimal_value = best_fitness;
end

请注意，这些代码示例仅提供了一个基本框架，实际应用中需要根据具体的优化问题定制`fitness_func`和`generateRandomNeighbor`函数。