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

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parag patil
parag patil 2021-4-17
评论： parag patil 2021-4-18
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 ?

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Matt J
Matt J 2021-4-17
编辑：Matt J 2021-4-17
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.

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