I am working on a binary non-linear programming. The objective function is exponential. For example,

Maximize -exp(-(2*(x(1)+x(2)))^1.2)*exp(-(1*(x(3)+x(4)))^1.2)

Constraint: 
x(1)+x(3)=1;
x(2)+x(4)=1;
x(1)+x(2) >= x(3)+x(4)

x(i)={0 or 1}, 
i=1, 2, 3, 4

I never solve the binary non-linear programming before. Shall I use GA or try some solvers? But GA can not specify the binary constraints. 

I tried minlp from tomlab. But the Hessian matrix is too complex to compute and 1/0^0.8 can occur, which will make the result inf. 

Anyone can help?? Thanks a lot. 

Is this the size of problems you really intend to solve? In tjhat case, just solve it by enumeration. In this case, you immediately see that out of the 16 combinations, there is only one feasible, X = [1 1 0 0]

"John  Wang" <huiwang223@gmail.com> wrote in message <higt7n$gmp$1@fred.mathworks.com>...
> I am working on a binary non-linear programming. The objective function is exponential. For example,
> 
> Maximize -exp(-(2*(x(1)+x(2)))^1.2)*exp(-(1*(x(3)+x(4)))^1.2)
> 
> Constraint: 
> x(1)+x(3)=1;
> x(2)+x(4)=1;
> x(1)+x(2) >= x(3)+x(4)
> 
> x(i)={0 or 1}, 
> i=1, 2, 3, 4
> 
> I never solve the binary non-linear programming before. Shall I use GA or try some solvers? But GA can not specify the binary constraints. 
> 
> I tried minlp from tomlab. But the Hessian matrix is too complex to compute and 1/0^0.8 can occur, which will make the result inf. 
> 
> Anyone can help?? Thanks a lot. 

Thanks for the reply. 

This is a just an example. The actual problem size will be bigger. The variable will be 25. Then that will be 2^25 possible combinations. Enumeration probably is a good way to do that.

John 

&#8364;&#8364;&#8364;"Johan Löfberg" <loefberg@control.ee.ethz.ch> wrote in message <hihej9$be4$1@fred.mathworks.com>...
> Is this the size of problems you really intend to solve? In tjhat case, just solve it by enumeration. In this case, you immediately see that out of the 16 combinations, there is only one feasible, X = [1 1 0 0]
> 
> "John  Wang" <huiwang223@gmail.com> wrote in message <higt7n$gmp$1@fred.mathworks.com>...
> > I am working on a binary non-linear programming. The objective function is exponential. For example,
> > 
> > Maximize -exp(-(2*(x(1)+x(2)))^1.2)*exp(-(1*(x(3)+x(4)))^1.2)
> > 
> > Constraint: 
> > x(1)+x(3)=1;
> > x(2)+x(4)=1;
> > x(1)+x(2) >= x(3)+x(4)
> > 
> > x(i)={0 or 1}, 
> > i=1, 2, 3, 4
> > 
> > I never solve the binary non-linear programming before. Shall I use GA or try some solvers? But GA can not specify the binary constraints. 
> > 
> > I tried minlp from tomlab. But the Hessian matrix is too complex to compute and 1/0^0.8 can occur, which will make the result inf. 
> > 
> > Anyone can help?? Thanks a lot.