SOS Type I

Answered

Ebru Angun

• October 08, 2019 07:36

Hi to all,

My question is that there are two variables, say z and s, such that 0 <= z <= 1 and s >= 0, and they define to form a special ordered set of type I (SOS Type I).

How does Gurobi handle this issue?

Ebru

 

 

 

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• Official comment

  

  Simranjit Kaur

  Gurobi Staff

  • December 06, 2024 00:53

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
• 

  Tobias Achterberg

  Gurobi Staff

  • October 08, 2019 10:06

  SOS1 constraints are handled via branching. If you have a solution that would be feasible without the SOS1 constraint but that violates this SOS1 constraint (i.e., both z and s are non-zero), then Gurobi creates two child nodes, setting z = 0 in one child and s = 0 in the other child.

  If z is binary and s has a finite upper bound u, i.e., z \in {0,1} and 0 <= s <= u, then Gurobi may also translate this SOS1 constraint into a linear constraint using a big-M formulation, namely

     s <= (1-z)u

  which means

     s + zu <= u.

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• 

  Ebru Angun

  • October 08, 2019 10:10

  

  

  

  Thank you

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