Integer Problem Solving with two boolean selection variables

Question

I am trying to solve a two dimensional combinatorial problem. Hereis my input space {{RA1,RA2},{RB1,RB2},{RC1,RC2}} and i have to choose two out of three elements{A,B,C} and one out of two possible variations for each of these elements {1,2}. I have an objective function to maximize and i have some constraints. Based on these i have to make above selections. Can anyone please tell me if there is any optimization algorithm already available which serves my purpose. In reality i have a huge input space, so any existing algorithm is prefered

Answer 1

Sure, try integer linear programming. Let $x_{RA1}$ be a zero-or-one variable that is 1 if you select RA1, or 0 if you don't. Then each of your constraints can be expressed as linear inequalities with these variables. You can then try applying an off-the-shelf ILP solver.

There are a bunch of other questions on this site with further examples of using ILP to solve combinatorial problems (e.g., Express boolean logic operations in zero-one integer linear programming (ILP)), so feel free to look around.