How to find all the possible feasible solutions to a integer linear programme?

I have following question:

1. # of decision variables : 20; These can take the values {0,1} (integers)
2. I have linear inequality constraints ( functions of above decision variables)
3. I do not have any objective function.

Can I get set of all feasible solutions ( which just satisfty the linear inequality / equality constraints ? I do not want to optimize anything. I want to have the set of all feasible points.

Is it doable ?

Answer 1

[Matt J]

For R^20, yes. Just do an exhaustive search,

[x{1:20}]=ndgrid([0,1]);
x=reshape( cat(21,x{:}) ,[],20).';

feasible = x(:, all(A*x<=b+tolerance,1) ); %20xN matrix of feasible solutions.

[parag patil]

Thank you for your answer. It is helpful.