I don’t have integer variables in my real model; it only contains binary variables and continuous variables. That’s why I just formulated simple model consisting of only binary variables. Now, if I want to use systematic enumeration procedure do I need extra binary variables that continuously add cuts to my model?

If you can provide formulation of attached model and the question I asked, it will be much easier for me to understand the concept.

You have a model with binary variables, so the cuts are pretty easy. It is a bit messier with integer variables. Essentially, for a given solution xbar(i), you can make sure that solution is not repeated by counting the differences between xbar and x and bounding this below by 1:

As you accumulate more solutions xbar, you add more constraints to the model.

Another way to do this that doesn’t involve adding any cuts is to use solver-specific features that enumerate all solutions and store them in a solution pool.

I really appreciate your suggestions and formulations.

Steve, I think you forget to attach the second model because the second file is only GDX.

I have made a formulation that systematically adds cuts to model and finds all feasible solution and terminates as soon solution become infeasible. However, I think there is still one problem. If you notice equation “cut” in the model, for each i, two new indices (actually alias) has to introduce in the equation. Now if the members of the set i increases from two to three, this means 4 indices are needed to add according to the current formulation.
Is there any way to reduce the number of indices by loops or some other strategy?
I also attached models, the first model is when i has only two members and later is when i has 3 members. You can notice that how the number of indices grows by increasing the members of i.