matlab 模拟退火算法tsp

以下是一个使用模拟退火算法解决TSP问题的MATLAB实现示例：

% TSP问题求解的模拟退火算法
% 使用方法：[route, distance] = tsp_simulated_annealing(distance_matrix, initial_temperature, final_temperature, cooling_rate)
% 输入参数：
%   - distance_matrix: 距离矩阵，即各个城市之间的距离矩阵，其中distance_matrix(i,j)表示第i个城市到第j个城市的距离
%   - initial_temperature: 初始温度
%   - final_temperature: 终止温度
%   - cooling_rate: 降温速率
% 输出参数：
%   - route: 最优路径，即访问所有城市的最优顺序
%   - distance: 最优路径的总长度

function [route, distance] = tsp_simulated_annealing(distance_matrix, initial_temperature, final_temperature, cooling_rate)
    n_cities = size(distance_matrix, 1); % 城市数量
    current_route = randperm(n_cities); % 初始路径
    current_distance = get_path_distance(current_route, distance_matrix); % 初始路径长度
    best_route = current_route; % 最优路径
    best_distance = current_distance; % 最优路径长度
    temperature = initial_temperature; % 当前温度
    while temperature > final_temperature
        for i = 1 : n_cities
            new_route = current_route;
            % 随机交换两个城市
            j = randi(n_cities);
            while j == i
                j = randi(n_cities);
            end
            new_route([i, j]) = new_route([j, i]);
            new_distance = get_path_distance(new_route, distance_matrix); % 新路径长度
            % 判断是否接受新路径
            delta_distance = new_distance - current_distance;
            if delta_distance < 0
                % 新路径更优，直接接受
                current_route = new_route;
                current_distance = new_distance;
                if new_distance < best_distance
                    % 更新最优路径
                    best_route = new_route;
                    best_distance = new_distance;
                end
            else
                % 根据Metropolis准则接受新路径
                p = exp(-delta_distance / temperature);
                if rand() < p
                    current_route = new_route;
                    current_distance = new_distance;
                end
            end
        end
        temperature = temperature * cooling_rate; % 降温
    end
    route = best_route;
    distance = best_distance;
end

% 计算路径长度
function distance = get_path_distance(route, distance_matrix)
    n_cities = size(distance_matrix, 1);
    distance = 0;
    for i = 1 : n_cities - 1
        distance = distance + distance_matrix(route(i), route(i+1));
    end
    distance = distance + distance_matrix(route(n_cities), route(1));
end

使用示例：

% 构造距离矩阵
distance_matrix = [
    0, 1, 2, 3;
    1, 0, 4, 5;
    2, 4, 0, 6;
    3, 5, 6, 0;
];
% 调用模拟退火算法求解TSP问题
[route, distance] = tsp_simulated_annealing(distance_matrix, 100, 0.1, 0.99);
disp(route); % 输出最优路径
disp(distance); % 输出最优路径长度