clear;clc;
%?hopfield神經(jīng)網(wǎng)絡(luò)
%?問題擬定為在網(wǎng)格上隨機(jī)選取N個(gè)點(diǎn)作為城市，然后計(jì)算出TSP問題的最優(yōu)解
%（1）初始化Hopfield神經(jīng)網(wǎng)絡(luò)的初值
city_num=11;
%?懲罰參數(shù)A和D
%?A=city_num^2;
%?D=city_num/2;
A=1.5;
D=1;
%初始電壓
u_0=0.02;
%步長(zhǎng)
step=1;
%最大迭代次數(shù)
iter=0;
MAX=10000;
%最小能量最小距離
E_min=10000;
d_min=10000;
%（2）生成網(wǎng)格，并計(jì)算n個(gè)城市之間的距離矩陣Dxy
%隨機(jī)生成城市坐標(biāo)
%?city_pos_1=randi（[19]1city_num）;
%?city_pos_2=randperm（9）;
city_perm=randperm（81）;
city_perm=city_perm（11:city_num）;
city_pos_1=（floor（city_perm./9）+1）.*0.1;
city_pos_2=（mod（city_perm9）+1）.*0.1;
city_pos=[city_pos_1;city_pos_2（11:city_num）];
%?city_pos=[1122;1212];
%?citys=load（‘8.txt‘）;
%
%?city_num=8;
%?city_pos=citys‘;
%計(jì)算城市間距
d=zeros（city_num）;
for?i=1:city_num
????for?j=1:city_num
????????d（ij）=（city_pos（:i）-city_pos（:j））‘...
????????????*（city_pos（:i）-city_pos（:j））;
????????d（ij）=d（ij）^（1/2）;
????end
end
%畫出網(wǎng)格
hold?on;
plot（city_pos（1:）city_pos（2:）‘Ko‘）;
for?k=1:city_num
????str=[‘???city‘?num2str（k）?‘‘];
????text（city_pos（1k）city_pos（2k）str）;
end
%?set（gca‘XLim‘[0?city_num+1]‘YLim‘[0?city_num+1]）;
set（gca‘XLim‘[0?1]‘YLim‘[0?1]）;
grid?on;
%%
tic
%（3）初始化神經(jīng)網(wǎng)絡(luò)的輸入狀態(tài)
%?U=zeros（city_num）;
U_0=zeros（city_num）+u_0;
%?delta=2*rand（city_num）-1;%隨機(jī)項(xiàng)
delta=（2*rand（city_num）-1）/10;%隨機(jī)項(xiàng)
U=（0.5*log（city_num-1））.*U_0+delta;
V=0.5*（1+tanh（U/u_0））;

V_col=sum（V1）;%列和
V_row=sum（V2）;%行和
Best_Route=[E_min;d_min;zeros（city_num1）];
while?iter~=MAX
????%（4）利用動(dòng)態(tài)方程計(jì)算輸入狀態(tài)的增量，并更新神經(jīng)網(wǎng)絡(luò)下一個(gè)時(shí)刻的狀態(tài)
????%?計(jì)算增量dU
%?????if?iter==0
%?????????U_c=U;
%?????end??
????dU=zeros（city_num）;
????for?l=1:city_num
????????for?m=1:city_num
????????????m_0=m+1;
????????????m_1=m-1;
????????????if?m==city_num
????????????????m_0=1;
????????????end
????????????if?m==1
????????????????m_1=city_num;
????????????end
????????????dU（lm）=-A*（V_col（m）+V_row（l）-2）-...
????????????????D*d（l:）*V（:m_0）;
%?????????????dU（lm）=-A*（V_row（m）-U（lm））-B*（V_col（l）-U（lm））-...
%?????????????????C*（sum（V_row）-city_num）-D*（d（l:）*U（:m_0）+d（l:）*U（:m_1））;
????????end
????end
????%更新U
????U=U+dU*step;
????V=0.5*（1+tanh（U/u_0））;
????%（5）計(jì)算當(dāng)前的能量函數(shù)E
????V_col=sum（V1）;%列和
????V_row=sum（V2）;%行和
????part_1=sum（（V_col-1）.^2）;
????part_2=sum（（V_row-1）.^2）;
????part_3=0;
????for?n=1:city_num
????????for?o=1:city_num
????????????for?p=1:city_num
????????????????p_0=p+1;
????????????????if?p==city_num
????????????????????p_0=1;
????????????????end
????????????????part_3=part_3+V（np）*V（op_0）*d（no