Max Function

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Hussein Sharadga

2022年10月24日 08:47

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I have an issue using max function in Gurobi. I know that np.max (np is for numpy) will not work fine.

I learned that I should use the max_ function of gurobi and add some auxiliary variables but I am still not sure how to do it for my problem: The max function is applied on a vector in my problem.

Below you can find the main lines in the code. (Please see max function in obj1 and obj2)

 

m=gp.Model()
muu=m.addVar(vtype='C',lb=-GRB.INFINITY,  name='muu')  # 
A=m.addVars(n, lb=-GRB.INFINITY, vtype='C', name='A')
B=m.addVars(n, lb=-GRB.INFINITY, vtype='C', name='B')
C=m.addVars(len(t), lb=-GRB.INFINITY, vtype='C', name='C')
D=m.addVars(len(t), lb=-GRB.INFINITY, vtype='C', name='D')

obj1=gp.quicksum(np.max((x[i]-muu-C[i]-D[i]),0)         for i in range(len(t)))
obj2=gp.quicksum(np.max(-1*(x[i]-muu-C[i]-D[i]),0)  for i in range(len(t))) 
m.setObjective((T*obj1+(1-T)*obj2)/len(t)) 
  
m.addConstrs( C[i]== gp.quicksum(A[k]*matrix1[i][k] for k in range (n)) for i in range (len(t))) 
m.addConstrs( D[i]== gp.quicksum(B[k]*matrix2[i][k] for k in range (n)) for i in range (len(t))) 
m.optimize()

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  Simranjit Kaur

  • Gurobi Staff

  2025年11月16日 23:26

  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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  Jaromił Najman

  • Gurobi Staff

  2022年10月24日 15:06 編集済み

  I learned that I should use the max_ function of gurobi and add some auxiliary variables but I am still not sure how to do it for my problem: The max function is applied on a vector in my problem.

  You have to introduce an auxiliary variable for every \(\texttt{x[i]-muu-C[i]-D[i]}\) and \(\texttt{-x[i]+muu+C[i]+D[i]}\) term and then use the addGenConstrMax method. Something like the following should work

  m=gp.Model()
  muu=m.addVar(vtype='C',lb=-GRB.INFINITY,  name='muu')  # 
  C=m.addVars(len(t), lb=-GRB.INFINITY, vtype='C', name='C')
  D=m.addVars(len(t), lb=-GRB.INFINITY, vtype='C', name='D')
  # add auxiliary variables
  auxvarpos=m.addVars(len(t), lb=-GRB.INFINITY, vtype='C', name='auxvarpos')
  auxvarneg=m.addVars(len(t), lb=-GRB.INFINITY, vtype='C', name='auxvarneg')
  maxobj1=m.addVars(len(t), lb=-GRB.INFINITY, vtype='C', name="maxobj1")
  maxobj2=m.addVars(len(t), lb=-GRB.INFINITY, vtype='C', name="maxobj2")
  # add auxiliary equality constraints
  m.addConstrs((auxvarpos[i] ==  x[i]-muu-C[i]-D[i]) for i in range(len(t)), name="auxconstrpos")
  m.addConstrs((auxvarneg[i] == -x[i]+muu+C[i]+D[i]) for i in range(len(t)), name="auxconstrneg")
  # add constraints maxobj1 = max(auxvarpos,0), maxobj2 = max(auxvarneg,0)
  m.addConstrs((maxobj1[i] == gp.max_(auxvarpos[i], constant=0) for i in range(len(t)), name="maxconstrobj1")
  m.addConstrs((maxobj2[i] == gp.max_(auxvarneg[i], constant=0) for i in range(len(t)), name="maxconstrobj2")
  
  obj1=gp.quicksum( maxobj1[i] for i in range(len(t)))
  obj2=gp.quicksum( maxobj2[i] for i in range(len(t)))

  Best regards, 
  Jaromił

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  Hussein Sharadga

  2022年10月24日 20:48

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  Thank you so much!

  I do appreciate your time.

   

  Hussein

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