How do I set subset of variables to constant value or disable optimization

Answered

Danning Xie

• February 11, 2022 15:09
• Edited

I am trying to find solution for binary variable `x_{i,j}`, where `i =1,2,...,n` and `j=1,2,... m`. 

x is defined as:

x = model.addVars(n,m, vtype=GRB.BINARY)

However, I want to disable the optimization on a subset of `x_{i,j}`, i.e., set them to constant 0. In this way, the search space will be much smaller. 

 

I read the document and didn't find anything. Is there a good way to do this? Alternatively, I can re-define the variable. Say if n=10, m=10, the size for `x_{i,j}` will be 100. If I want to set 70 of them to constant 0 and disable the optimization of them, I can define `y_k` with the size of 30, and only do optimization on y. And I will need to define another map to record the mapping relations between x and y. In this way, the search space is only 30. 

 

I wonder if there is a more elegant way to lock some of the variables?

 

Thank you!

 

0

• 

  Jonasz Staszek

  Community Moderator

  • February 11, 2022 15:23
  • Edited

  

  

  

  Hi!

  This can be efficiently done in two ways:

  1. Add a constraint and set a variable to zero:

  model.addLConstr(x[n,m] == 0)

  By the way, you can sum all the variables you want to be fixed to zero on the left-hand side instead of having variable-many constraints.

  2. Set the bounds on variables you wish to "lock":

  x[n,m].lb = 0
  x[n,m].ub = 0

  This needs to be done for each variable individually.

  Hope this helps.

  Best regards
  Jonasz

  0
• 

  Danning Xie

  • February 11, 2022 15:44

  

  

  

  Hi,

  Thank you! 

  I wonder by the design of Gurobi, will these two methods help accelerate the optimization or reduce the search space?

   

   

  Danning

  0
• 

  Jonasz Staszek

  Community Moderator

  • February 11, 2022 16:05

  

  

  

  This question is better suited to Gurobi staff.

  From my own experience, the variables which may only assume one value are removed in the presolve and hence reduce the search space. The more variables you "fix", the smaller the search space becomes and hence you can hope for a faster solution process.

  0
• 

  Jaromił Najman

  Gurobi Staff

  • February 11, 2022 16:37

  Jonasz is correct. Fixed variables are removed in the presolve step and thus reduce the search space, which in general often results in a faster optimization process.

  Best regards, 
  Jaromił

  0
• 

  Danning Xie

  • February 11, 2022 17:53

  

  

  

  Thank you Jonasz and Jaromił. This helps a lot.

   

  Danning

  0

Please sign in to leave a comment.