Function applied to variable for more flexible domain

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Alexander Chen

2024年07月23日 23:16 編集済み

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Optimizing a problem f(x), where 0.0 <= x <=1 .0

Is it possible to achieve below when solving x?

when x < threshold, x== 0

when x >= threshold, x== x

関連

• Semi-continuous

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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:22

  This post is more than two 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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  Simranjit Kaur

  • Gurobi Staff

  2024年07月24日 00:29

  You can define x as a semi-continuous variable. A semi-continuous variable has the property that it takes a value of 0 or a value between the specified lower and upper bounds. With the Python API, you can define your x variable as follows:

  x = model.addVar( lb = threshold, vtype = "S", name ="x")

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  Alexander Chen

  2024年07月24日 14:28

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  Thank you. I'll try it out

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  Alexander Chen

  2024年10月07日 16:16

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  Have checked that it would work as expected. Would it be possible to mix it with the continuous variable? For example, set x1-x5 to be semi-continuous and the rest to be just continuous

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  Simranjit Kaur

  • Gurobi Staff

  2024年10月07日 21:48

  Yes, a model can have both semi-continuous and continuous variables.

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  Alexander Chen

  2024年10月07日 22:10

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  Sorry I meant mixing semi-continuous and continuous for a variable with length n

  That sounds like just using different ub/lb for each x_i. Could you confirm?

  For example,

  n = 10
  threshold = 0.2
  lb = np.zeros(n)
  lb[0] = threshold
  x = model.addVar(n, lb=lb , ub=1.0, vtype="S", name="x")

  But if want to pin my x_i (ub and lb are the same), can it still by any chance bring it to 0?

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  Simranjit Kaur

  • Gurobi Staff

  2024年10月08日 01:02 編集済み

  One approach to do this would be to set the "vtype" attribute for the variables according to the types you want. In the example below, x[0], x[1], and x[2] will be semi-continuous variables with lower bounds of 1, and x[3] and x[4] will be continuous variables with the default lower bound of zero.

  lb = [1,1,2,0,0]
  x = m.addVars(5, lb=lb, vtype=["S" for _ in range(3)] + ["C" for _ in range(2)], name="x")

  I hope this helps.

  Best regards,
  Simran

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  Alexander Chen

  2024年10月08日 14:40

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  That's what I'm looking for. Thank you!

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