How to write max function in models

Answered

Ankit khare

• January 25, 2021 04:00
• Edited

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

0

• 

  Jaromił Najman

  Gurobi Staff

  • January 26, 2021 11:20
  • Edited

  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

   

  2
• 

  Ankit khare

  • January 30, 2021 01:54
  • Edited

  

  

  

  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] )

   

   

  0
• 

  Jaromił Najman

  Gurobi Staff

  • February 01, 2021 08:32
  • Edited

  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

  0
• 

  Shiyang Huang

  • October 31, 2022 16:25

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

  0
• 

  Jaromił Najman

  Gurobi Staff

  • November 02, 2022 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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