Encoding used for SOS2 reformulation
Controls the automatic reformulation of SOS2 constraints. Such constraints can be handled directly by the MIP branch-and-cut algorithm, but they are often handled more efficiently by reformulating them using binary or integer variables. There are several diffent ways to perform this reformulation; they differ in their size and strength. Smaller reformulations add fewer variables and constraints to the model. Stronger reformulations reduce the number of branch-and-cut nodes required to solve the resulting model.
Options 0 and 1 of this parameter encode an SOS2 constraint using a formulation whose size is linear in the number of SOS members. Option 0 uses a so-called multiple choice model. It usually produces an LP relaxation that is easier to solve. Option 1 uses an incremental model. It often gives a stronger representation, reducing the amount of branching required to solve harder problems.
Options 2 and 3 of this parameter encode the SOS2 using a formulation of logarithmic size. They both only apply when all the variables in the SOS2 are non-negative. Option 3 additionally requires that the sum of the variables in the SOS2 is equal to 1. Logarithmic formulations are often advantageous when the SOS2 constraint has a large number of members. Option 2 focuses on a formulation whose LP relaxation is easier to solve, while option 3 has better branching behaviour.
The default value of -1 chooses a reformulation for each SOS2 constraint automatically.
Note that the reformulation of SOS2 constraints is also influenced by the PreSOS2BigM parameter. To shut off the reformulation entirely you should set that parameter to 0.
For examples of how to query or modify parameter values from our different APIs, refer to our Parameter Examples.
Please refer to this section for more information on SOS constraints.