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
