How to write max function in models

回答済み

Ankit khare

2021年01月25日 04:00 編集済み

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I have tried Model.addGenConstrMin() and max_ . But couldn't able to run the model.

what i want is to write following line of Python-Cplex into Python-Gurobi

Python-Cplex - mdl.minimize(mdl.sum(mdl.max((ct[nStage,j]-D[j-1]),0) for j in job))

 

Cplex-OPL- minimize sum(j in job) maxl((ct[nStage][j]-D[j]),0);

 

Lingo:  @SMAX((CT[nStage][j]-D[j]),0);

 

How to write this line in Python-gurobi

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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 03:01 編集済み

  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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  Jaromił Najman

  • Gurobi Staff

  2021年01月26日 11:20 編集済み

  Hi Ankit,

  The max function works a bit different in Gurobi. It is used to define a max constraint

  \[ z = \max\{x_1,x_2,1,2\},\]

  where \(z,x_1,x_2\) are optimization variables and \(1,2\) constant values. The term \(\texttt{ct[nStage,j]-D[j]}\) describes a linear expression and not an optimization variable. Thus, in order to model the objective function, you have to introduce 2 additional auxiliary variables for each \(j\). Then, your code might look something like

  import gurobipy as gp
  from gurobipy import GRB
  
  m = gp.Model('test')
  # some arbitrarily picked values
  job = [1,2,3,4,5]
  nStage = 3 
  
  ct   = m.addVars(4, job, vtype=GRB.CONTINUOUS, name="ct")
  D    = m.addVars(job, vtype=GRB.CONTINUOUS, name="D")
  # define auxiliary variables
  aux1 = m.addVars(job, vtype=GRB.CONTINUOUS, name="aux1")
  aux2 = m.addVars(job, vtype=GRB.CONTINUOUS, name="aux2")
  
  # add constraints defining ct_j - D_j = aux1_j
  m.addConstrs( (ct[nStage,j]-D[j] - aux1[j] == 0 for j in job), name="aux_constr1")
  # add constraints defining aux2_j = max(aux1_j, 0)
  m.addConstrs( (aux2[j] == gp.max_([aux1[j],0.0]) for j in job), name="aux_constr2")
  
  # set objective to be the sum of all aux2 variables
  m.setObjective( gp.quicksum(aux2[j] for j in job))

  Best regards,
  Jaromił

   

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  Ankit khare

  2021年01月30日 01:54 編集済み

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  Thanks for the reply. It worked.

  I am facing the same problem with one constraint.

   mdl.add_constraints(ct[g,j1])>= mdl.max(ct[g-1,j1], ct[g,j]) + PT[g-1][j1-1] for f in factory for j in job for j1 in job if j1!=j for g in stage if g>1 for i in machine[g-1] ) 

   

  where ct is the decision variable. I tried as follows but couldn't able to run it

   

  First approach:

   

  mdl.addConstrs(ct[g,j1] >= gp.max_(ct[g-1,j1],ct[g,j]) + PT[g-1][j1-1] for f in factory for j in job for j1 in job if j1!=j for g in stage if g>1 for i in machine[g-1] )

   

  Second approach:

   

  mdl.addConstrs((aux3[g,j] == gp.max_(ct[g-1,j1],ct[g,j]) for j in job for j1 in job if j1!=j for g in stage if g>1), name="aux_constr3")

   

  mdl.addConstrs(ct[g,j1] >= aux3[g,j] + PT[g-1][j1-1] for f in factory for j in job for j1 in job if j1!=j for g in stage if g>1 for i in machine[g-1] )

   

   

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  Jaromił Najman

  • Gurobi Staff

  2021年02月01日 08:32 編集済み

  Hi Ankit,

  The max_() function has to be used in an equality constraint. Thus, your second approach is the way to go. Could you provide the error message and (if possible) a minimal working example? How do you define your variables \(\texttt{ct}\)?

  Best regards,
  Jaromił

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  Shiyang Huang

  2022年10月31日 16:25

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  Does Gurobi linearize max_ constraints automatically? could this lead to slower computation?

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  Jaromił Najman

  • Gurobi Staff

  2022年11月02日 08:33

  Does Gurobi linearize max_ constraints automatically?

  Yes.

  could this lead to slower computation?

  Do you mean in comparison to treating the \(\max\) function as a nondifferentiable function? It is possible that there are cases where treating the \(\max\) function without linearization via additional binary variables and auxiliary constraints might be beneficial. I would say that linearization should work very well in most of cases.

   

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