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

Ongoing

Somreeta Pramanik

October 05, 2022 13:00 Edited

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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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  Maliheh Aramon

  • Gurobi Staff

  October 08, 2022 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

  October 10, 2022 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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