Why Objective must be liearn for multi-objective model in Gurobi ?

Answered

Laaziz Lahlou

April 25, 2020 17:27

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Hi all,

I have a multi-objective optimization problem where in some of the cost functions I do have a product of two decision variables. The form of the optimization problem embeds the assignment problem.

I first linearized the product of the two decision variables but Gurobi returns the following error message :

gurobipy.GurobiError: Objective must be linear for multi-objective model.

Is there a way to get rid of this issue ? I mean how could I solve my problem from the multi-objective perspective with this product of the two decision variables ?

Could anyone point out some technical solutions ?

Regards

Laaziz

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 03:14 Edited

  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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  Silke Horn

  • Gurobi Staff

  April 27, 2020 06:08

  Hi Laaziz,

  For multi-objective models, all objectives must be linear, but you should be able to work around this by linearizing the non-linear term. E.g. if your objective contains the term x*y, add a new variable z and replace x*y by z in the objective. Then add an additional constraint x*y == z. Note that this must be a constraint in the model, not a Python assignment. E.g.

  model.addConstr(x*y == z)

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  Laaziz Lahlou

  April 27, 2020 22:20 Edited

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  Hi Horn,

  Surprisingly, it works without the linearization method I had to use.

  Thanks

  Laaziz

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