Linearizing Max function in constraint

回答済み

Joao Coelho

2023年07月11日 09:27

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I'm trying to linearize the following constraints in python. 

mdl = Model('MTHFVRPTW')

rtkw = mdl.addVars(vehicles, trips, vtype=GRB.CONTINUOUS) #return time of trip w of vehicle k
aac = mdl.addVars(vehicles, customers, trips, vtype=GRB.CONTINUOUS) #arrival at customer with veh k on trip w

#13
mdl.addConstrs(rtkw[k,w] >= max(aac[k,i,w], earliest[i]) for i in customers for k in vehicles for w in trips)
#14 
mdl.addConstrs(aac[k,j,w] >= max(aac[k,i,w], earliest[i])  for i,j in customers for k in vehicles for w in trips)

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  Joao Coelho

  2023年07月11日 09:58

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  the list earliest is a parameter of my problem, not a variable

   

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  Maliheh Aramon

  • Gurobi Staff

  2023年07月13日 02:39

  Hi Joao, 

  Let us assume that you would like to implement a constraint in the form \(\max(x, c)\) with \(c\) being a constant value. 

  • You need to fist define an auxiliary variable \(y\)
  • You can then use the method Model.addGenConstrMax() (or general constraint helper function gurobipy.max_()) to implement the relationship \(y = \max(x, c)\). 
  • You can then use \(y\) in place of \(\max(x, c)\) in any other constraint where the \(\max\) function appears. 

  Best regards,

  Maliheh

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