Originally posted by: nlp7

Hi,

I have some logical constraints in my formualation, specifically if some binary is zero, then a specific continuous must be zero too.

I modeled it both with a bigM that I calculated by myself, and with the CPLEX API that allows for direct modeling of logical constraints ( IloIfThen() ). Both of the approaches yield the same result, however the second one (IloIfThen), is 3 times slower!

Is there any way that we can provide to CPLEX some insight about a reasonable BigM so that we can accelerate things up? I would like to use the native logical description of the problem, because it makes it so much more readable, but really I cannot sacrifice that much of the performance.

Were we supposed to use the IloIfThen only when we have no clue about a reasonable BigM?

Out of curiosity, in the version using IloIfThen did you specify an upper bound for the continuous variable in each if-then constraint? Presumably this would be the same value used as M in the big M version.

Originally posted by: nlp7

My bigM constraint is like -Mb<=c<=Mb where b is {0,1}, and c belongs to [-1,000, 1,000]. The M is lets say 10,000.

The same bounds are also given to the b,c variable when I am writing the IloIfthen(env, b=0, c=0)

If the domain of c is [-1,000, +1,000] then you might as well use M = 1,000 rather than M = 10,000 in the big M approach. With the same bounds specified for c in the if-then approach, I'm surprised that performance is worse. If anything, it should be faster, since internally CPLEX should be treating IloIfThen(env, b = 0, c = 0) as -1000b <= c <= 1000b, which is tighter than -10,000b <= c <= 10,000b.

Originally posted by: nlp7

This was my expectation as well. As you pointed out my big-M is not even the tightest possible, yet CPLEX seems to work much better with the big-M's. From the lp file, I see that it reformulates the Iloifthen as SOS constraints, introducing extra 0,1 variables, but I have no clue what it does with this internally during the solution.