MILP technique against SOS2 method: different result in two same models
Dear all
Dear all
I have a MILP model with some SOS2 constraints. I implement the SOS2 constraints with two approaches including SOS2 variable definition using native SOS2 provided by the solver and a MILP technique enforcing SOS2 constraints using integer variables. While the both models follow the same branching procedure in the beginning, the native SOS2 presents a premature convergence albeit with zero integrality gap resulting a different solution compared to the MILP technique outcome. Actually, the MILP technique converges to a better solution. Interestingly, for a smaller case study the results are exactly similar maybe suggesting that both the models are equivalent. As the MILP model is convex in the relaxed form (relaxing integer values) it is expected that all MILP solution techniques converge to same solution. I could not found any parameters to set in SOS2 framework to further explore the problem space. What does the difference originate from?

Most likely the difference is due to poor model's numerics; in turn, this often leads to unstable solver's behaviour on such models.
Can you give some model stats here to begin with, namely, what is the range of affine coefficients and so on you see in Gurobi's log for both formulations?
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