Trouble in implementing `if` conditionals in Gurobi Python Objective Function

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Somreeta Pramanik

2022年10月05日 13:00 編集済み

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I have an objective function that has a if conditional in it. I am having trouble implementing it in Gurobi Python.

I want to maximize the utility using an objective function like-

U =1- erf(z), if z<=0

  = erf(z) otherwise

where z is an integer variable

Need urgent help. Any advice would be appreciated

Thanks,

Somreeta

 

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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年11月16日 23:27

  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 try Gurobot, our chatbot interface offering instant, expert-level support.
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  Maliheh Aramon

  • Gurobi Staff

  2022年10月08日 01:06

  Hi Somreeta, 

  If \(\mbox{erf}(z)\) is a linear function of \(z\) decision variable, you can define an auxiliary binary variable \(x\) where:

  \[\mbox{if}~~ z \leq 0 \rightarrow x = 1\] \[\mbox{if}~~ z \geq 1 \rightarrow x = 0\]

  The objective function can then be implemented as \(U = x \big(1-\mbox{erf}(z)\big) + (1-x) \mbox{erf}(z)\) which is quadratic. 

  Using contraposition, the conditional statements are equivalent to:

  \[\mbox{if}~~ x \neq 1  \rightarrow z \nleq 0 \mbox{, which implies: if} ~~ x = 0  \rightarrow z \geq 1\]

  \[\mbox{if}~~ x \neq 0  \rightarrow z \ngeq 1 \mbox{, which implies: if} ~~ x = 1  \rightarrow z \leq 0\]

  These constraints can be implemented using the Gurobi's API for indicator constraints.

  If \(\mbox{erf}(z)\) is a higher order function of \(z\), you can model it as a piecewise-linear objective. For more details, please check out the documentation on piecewise-linear objectives and the python example piecewise.py.

  Best regards,

  Maliheh

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  Somreeta Pramanik

  2022年10月10日 09:40

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  Thank you for the help. 

  I have a related question. As addGenConstrPow accepts a constant exponent, it does not accept k, which is an iterator variable.

  Is there an alternative way of doing it?

  Following is the code snippet,

  w=m.addVar(name="w")
  myAuxVar= m.addVar(vtype=GRB.CONTINUOUS, name="myAuxVar") 
  m.addConstr(myAuxVar==Lambda * w) 
  powconstr1= m.addGenConstrPow(myAuxVar, v, k, "pow2", "FuncPieces=1000")

  where k is an iterator variable

  I receive the following error message- Encountered an attribute error

  Thanks

  Somreeta

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