Originally posted by: SystemAdmin

Hi, everyone,

I have a question about the variables which are implied feasible. I am using BranchCallback and NodeCallback to propose the branch and bound rule. What I observed is that when I query both the feasibility status and the value of some binary variables, I found some variables are implied feasible and their values are 0 or 1 at the beginning of the branch and bound but later as the branch and bound goes, the values of them are neither 0 or 1, they are some positive fractional numbers like 0.35866, 0.53708 or something like that. Why does that happen? Should they be binding at either 0 or 1 in the presolve process and cannot be changed?

BTW: the parameter of cplex.EpInt is set to be 1e-07 and cplex.EpRHS is set to be 1e-04.
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Originally posted by: SystemAdmin

I double checked the manual, and it is said that

ImpliedFeasible indicates the variable or SOS has been presolved out. It will be feasible when all other integer variables or SOS are integer feasible.

So is it because some of the un-presolved variables are taking fractional number so that the implied feasible variables would take fractional number when a LP relaxation of the node is solved?
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Exactly. Consider, for example, a problem instance that includes two general integer variables x and y. It also features an equation

y - 3x = 0

Then, CPLEX can aggregate y := 3x, which means to substitute y for 3x everywhere in the model. If it then finds a feasible (or even optimal) solution to the reduced problem, x will be integral and thus it can just calculate y = 3x, which will also lead to an integral value.
Of course, it will happen all the time that CPLEX encounters LP relaxation solutions in which x is fractional. Consequently, y will also be fractional in those LP relaxation solutions.

Tobias
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