Multiplication of multiple variables

Answered

Michiel Maesen

December 10, 2019 10:48

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I’m currently using Gurobi optimizer for a cost optimization, but encounter a very annoying problem.

I would like to add constraints in which I multiply three variables, all binary, but results in a QuadExpr() error. Is there any way to overcome this issue?

Kind regards

Michiel

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  December 06, 2024 00:51

  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?.
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  Tobias Achterberg

  • Gurobi Staff

  December 10, 2019 11:54 Edited

  Gurobi only supports products of pairs of variables, not triples. To overcome this issue, you need to introduce auxiliary variables and build the more complex expression using those. For example, in order to model

  y = x1*x2*x3

  you could write

  z12 = x1*x2
  y = z12*x3

  For binary variables, this should just work out of the box. For non-binary variables, this is only supported since Gurobi 9.0, and only if you set the "NonConvex" parameter to 2.

  Regards,

  Tobias

   

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  Moritz Rettinger

  June 28, 2020 20:45 Edited

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  Is this still the only way to model prod() constraints?

   

  e.g. a == x1*x2*x3? I'm looking for something like quicksum just for products.

   

  Trying the solution above combined with https://support.gurobi.com/hc/en-us/community/posts/360057684331-invalid-expression-to-quad-expr-multiplication yields a quite ugly solution with a lot of dummy vars. Isn't there a simpler solution?

   

  Thanks in advance.

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  Richard Oberdieck

  • Gurobi Staff

  June 29, 2020 08:00

  Yes, unfortunately this is still the way to do it as of today.

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