Can we improve solution time when integer variables are determined by continuous variables?

Answered

Daniel Paleka

• March 02, 2020 13:03

If we have a mixed integer linear program over continuous variables X and discrete (say, binary) variables Y, where we know that for almost all fixed X there exists at most one feasible Y, can we tell that to Gurobi somehow? Would it improve optimization time? What about if we only want to solve the feasibility problem?

Thank you!

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• Official comment

  

  Simranjit Kaur

  Gurobi Staff

  • December 06, 2024 00:49

  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?.
• 

  Yuriy Zinchenko

  Gurobi Staff

  • March 05, 2020 02:43

  Hello Daniel,

  I do not think that in general one can exploit this information --the uniqueness of continuous portion of the solution as a function of discrete variables' values-- to speed up the solution process.  If possible, I would rather experiment with several alternative model formulations instead, to see if one formulation could be computationally superior to another.

  Regards,

   

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  Yuriy Zinchenko

  Gurobi Staff

  • March 06, 2020 01:16

  One more quick addition to the above, Daniel.

  It may also be the case that placing more emphasis on branching during the solve could be beneficial here. So, you may consider adding branchPriorities for some (important) binary variables, https://www.gurobi.com/documentation/9.0/refman/branchpriority.html

  and reducing the importance off cuts, https://www.gurobi.com/documentation/9.0/refman/cuts.html

  but without experimenting it is really impossible to predict the outcome.

   

  Regards.

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