Encoding used for SOS1 reformulation
Controls the automatic reformulation of SOS1 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 SOS1 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 SOS1 using a formulation of logarithmic size. They both only apply when all the variables in the SOS1 are non-negative. Option 3 additionally requires that the sum of the variables in the SOS1 is equal to 1. Logarithmic formulations are often advantageous when the SOS1 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 SOS1 constraint automatically.
Note that the reformulation of SOS1 constraints is also influenced by the PreSOS1BigM 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.