hopfield网络求解tsp问题matlab代码

好的，以下是一个基于Hopfield网络的TSP问题的Matlab代码：

% TSP问题的Hopfield网络求解

% 定义城市的坐标
cities = [
    60, 200;
    80, 200;
    80, 180;
    140, 180;
    20, 160;
    100, 160;
    200, 160;
    140, 140;
    40, 120;
    100, 120
];

% 计算城市之间的距离矩阵
num_cities = size(cities, 1);
distance_matrix = zeros(num_cities, num_cities);
for i = 1:num_cities
    for j = 1:num_cities
        distance_matrix(i, j) = sqrt(sum((cities(i,:) - cities(j,:)).^2));
    end
end

% 将距离矩阵转换成Hopfield网络的权重矩阵
weight_matrix = -0.5 * (distance_matrix.^2);
for i = 1:num_cities
    weight_matrix(i,i) = 0;
end

% 定义网络参数
threshold = 0;
num_iterations = 100;

% 初始化网络状态（随机生成一个可行路径）
current_path = randperm(num_cities);
current_state = zeros(1, num_cities*num_cities);
for i = 1:num_cities-1
    current_state(index(current_path(i), current_path(i+1), num_cities)) = 1;
end
current_state(index(current_path(num_cities), current_path(1), num_cities)) = 1;

% 迭代更新网络状态
for iter = 1:num_iterations
    update_indices = randperm(num_cities*num_cities);
    for i = 1:num_cities*num_cities
        index_to_update = update_indices(i);
        [city1, city2] = position(index_to_update, num_cities);
        if city1 ~= city2
            input_to_neuron = weight_matrix(city1, :) * current_state';
            input_to_neuron = input_to_neuron + weight_matrix(city2, :) * current_state';
            input_to_neuron = input_to_neuron - threshold;
            if input_to_neuron > 0
                current_state(index_to_update) = 1;
            else
                current_state(index_to_update) = 0;
            end
        end
    end
end

% 将最终状态转换成路径
final_path = zeros(1, num_cities);
for i = 1:num_cities
    for j = 1:num_cities
        if current_state(index(i, j, num_cities)) == 1
            final_path(i) = j;
            break;
        end
    end
end

% 绘制城市和路径
figure;
plot(cities(:,1), cities(:,2), 'o');
hold on;
for i = 1:num_cities-1
    x = [cities(final_path(i),1), cities(final_path(i+1),1)];
    y = [cities(final_path(i),2), cities(final_path(i+1),2)];
    plot(x, y, 'LineWidth', 2);
end
x = [cities(final_path(num_cities),1), cities(final_path(1),1)];
y = [cities(final_path(num_cities),2), cities(final_path(1),2)];
plot(x, y, 'LineWidth', 2);
hold off;

% 辅助函数
function ind = index(city1, city2, num_cities)
    ind = (city1-1)*num_cities + city2;
end

function [city1, city2] = position(ind, num_cities)
    city1 = ceil(ind/num_cities);
    city2 = mod(ind-1, num_cities) + 1;
end

这个代码实现了一个10个城市的TSP问题的Hopfield网络求解，并可视化了求解的结果。你可以根据需要进行修改和扩展。