连续Hopfield神经网络的优化——旅行商问题优化计算

连续Hopfield神经网络的优化——旅行商问题优化计算

%% 清空环境变量、定义全局变量
clear all
clc
global A D

%% 导入城市位置
load city_location

%% 计算相互城市间距离
distance = dist(citys,citys');

%% 初始化网络
N = size(citys,1);
A = 200;
D = 100;
U0 = 0.1;
step = 0.0001;
delta = 2 * rand(N,N) - 1;
U = U0 * log(N-1) + delta;
V = (1 + tansig(U/U0))/2;
iter_num = 10000;
E = zeros(1,iter_num);

%% 寻优迭代
for k = 1:iter_num  
    % 动态方程计算
    dU = diff_u(V,distance);
    % 输入神经元状态更新
    U = U + dU*step;
    % 输出神经元状态更新
    V = (1 + tansig(U/U0))/2;
    % 能量函数计算
    e = energy(V,distance);
    E(k) = e;  
end

 %% 判断路径有效性
[rows,cols] = size(V);
V1 = zeros(rows,cols);
[V_max,V_ind] = max(V);
for j = 1:cols
    V1(V_ind(j),j) = 1;
end
C = sum(V1,1);
R = sum(V1,2);
flag = isequal(C,ones(1,N)) & isequal(R',ones(1,N));

%% 结果显示
if flag == 1
   % 计算初始路径长度
   sort_rand = randperm(N);
   citys_rand = citys(sort_rand,:);
   Length_init = dist(citys_rand(1,:),citys_rand(end,:)');
   for i = 2:size(citys_rand,1)
       Length_init = Length_init+dist(citys_rand(i-1,:),citys_rand(i,:)');
   end
   % 绘制初始路径
   figure(1)
   plot([citys_rand(:,1);citys_rand(1,1)],[citys_rand(:,2);citys_rand(1,2)],'o-')
   for i = 1:length(citys)
       text(citys(i,1),citys(i,2),['   ' num2str(i)])
   end
   text(citys_rand(1,1),citys_rand(1,2),['       起点' ])
   text(citys_rand(end,1),citys_rand(end,2),['       终点' ])
   title(['优化前路径(长度：' num2str(Length_init) ')'])
   axis([0 1 0 1])
   grid on
   xlabel('城市位置横坐标')
   ylabel('城市位置纵坐标')
   % 计算最优路径长度
   [V1_max,V1_ind] = max(V1);
   citys_end = citys(V1_ind,:);
   Length_end = dist(citys_end(1,:),citys_end(end,:)');
   for i = 2:size(citys_end,1)
       Length_end = Length_end+dist(citys_end(i-1,:),citys_end(i,:)');
   end
   disp('最优路径矩阵');V1
   % 绘制最优路径
   figure(2)
   plot([citys_end(:,1);citys_end(1,1)],...
       [citys_end(:,2);citys_end(1,2)],'o-')
   for i = 1:length(citys)
       text(citys(i,1),citys(i,2),['  ' num2str(i)])
   end
   text(citys_end(1,1),citys_end(1,2),['       起点' ])
   text(citys_end(end,1),citys_end(end,2),['       终点' ])
   title(['优化后路径(长度：' num2str(Length_end) ')'])
   axis([0 1 0 1])
   grid on
   xlabel('城市位置横坐标')
   ylabel('城市位置纵坐标')
   % 绘制能量函数变化曲线
   figure(3)
   plot(1:iter_num,E);
   ylim([0 2000])
   title(['能量函数变化曲线(最优能量：' num2str(E(end)) ')']);
   xlabel('迭代次数');
   ylabel('能量函数');
else
   disp('寻优路径无效');
end

结果显示

最优路径矩阵

V1 =

     0     0     0     0     0     0     0     1     0     0
     0     0     0     0     0     0     0     0     1     0
     0     0     0     0     0     0     0     0     0     1
     0     0     0     0     1     0     0     0     0     0
     1     0     0     0     0     0     0     0     0     0
     0     1     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     1     0     0     0
     0     0     0     0     0     1     0     0     0     0
     0     0     1     0     0     0     0     0     0     0
     0     0     0     1     0     0     0     0     0     0

完毕