%整数规划分支定界算法matlab通用源程序
%各参数的意义同matlab优化工具箱的线性规划函数linprog
%调用前，输入参数要化成matlab的标准形式
[x,val]=kfz-f-3(n,f,a,b,aeq,beq,lb,ub)
x=zeros(n,1);
x1=zeros(n,1);
m1=2;
m2=1;
[x1,val1]=linprog(f,a,b,aeq,beq,lb,ub);
if (x1==0)
x=x1;
val=val1;
elseif (round(x1)==x1)
x=x1;
val=val1;
else
e1={0,a,b,aeq,beq,lb,ub,x1,val1};
e(1,1)={e1};
zl=0;
zu=-val1;
while (zu~=zl)
for c=1:1:m2
if (m1~=2)
if (cell2mat(e{m1-1,c}(1))==1)
e1={1,[],[],[],[],[],[],[],0};
e(m1,c*2-1)={e1};
e(m1,c*2)={e1};
continue;
end;
end;
x1=cell2mat(e{m1-1,c}(8));
x2=zeros(n,1);
s=0;
s1=1;
s2=1;
lb1=cell2mat(e{m1-1,c}(6));
ub1=cell2mat(e{m1-1,c}(7));
lb2=cell2mat(e{m1-1,c}(6));
ub2=cell2mat(e{m1-1,c}(7));
for d=1:1:n
if (abs((round(x1(d))-x1(d)))>0.0001)&(s==0)
s=1;
lb1(d)=fix(x1(d))+1;
if (a*lb1 s1=0;
end;
ub2(d)=fix(x1(d));
if (a*lb2 s2=0;
end;
end;
end;
e1={s1,a,b,aeq,beq,lb1,ub1,[],0};
e2={s2,a,b,aeq,beq,lb2,ub2,[],0};
e(m1,c*2-1)={e1};
e(m1,c*2)={e2};
end;
m1=m1+1;
m2=m2*2;
for c=1:1:m2
if (cell2mat(e{m1-1,c}(1))==0)
[x1,val1]=linprog(f,cell2mat(e{m1-1,c}( 2)),cell2mat(e{m1-1,c}(3)),cell2mat(e{m1-1,c}(4)),cell2mat(e{m1-1,c}(5)),cell2mat(e{m1-1,c}(6)),cell2mat(e{m1-1,c}(7)));
e1={cell2mat(e{m1-1,c}(1)),cell2mat(e{m1-1,c}(2)),cell2mat(e{m1-1,c}(3)),cell2mat(e{m1-1,c}(4)),cell2mat(e{m1-1,c}(5)),cell2mat(e{m1-1,c}(6)),cell2mat(e{m1-1,c}(7)),x1,val1};
e(m1-1,c)={e1};
end;
z=val1;
if ((-z) e1={1,[],[],[],[],[],[],[],0};
e(m1-1,c)={e1};
elseif (abs(round(x1)-x1) zl=z;
end;
end;
for c=1:1:m2
if (cell2mat(e{m1-1,c}(1))==0)
zu=cell2mat(e{m1-1,c}(9));
end;
end;
for c=1:1:m2
if (-cell2mat(e{m1-1,c}(9))>(-zu))
zu=cell2mat(e{m1-1,c}(9));
end;
end;
end;
for c=1:1:m2
if (cell2mat(e{m1-1,c}(1))==0)&(cell2mat(e{m1-1,c}(9))==zu)
x=cell2mat(e{m1-1,c}(8));
end;
end;
val=zu;
end;
