How to terminate a Linear program once i get a desired difference(say 1) between primal and dual solution?

Answered

Ishit Bajpai

July 20, 2022 08:26

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  Marika Karbstein

  • Gurobi Staff

  July 20, 2022 08:47

  Check this parameter MIPGap

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  Ishit Bajpai

  July 20, 2022 12:42 Edited

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  Thanks for your quick response.

  I am facing an issue while using the below code.

  m1.setParam('MIPGapAbs', 5)  
  m1.optimize()

  This code is not able to terminate the LP when |Primal(objective) - Dual(objective)| <= 5.

  Below are the log files,

  

  I think it should have terminated after 8th iteration but it keeps on going.

  Can you please point out the error?

   

  PS. This is a continuous model.

  Does gurobi have any methods like MIPGapAbs for continuous model ?

   

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  David Torres Sanchez

  • Gurobi Staff

  August 01, 2022 10:26 Edited

  Hi Ishit,
  
  If you can stick with Barrier (Method = 2), you can try BarConvTol, or more generally using OptimalityTol.
  You can check out more Parameters.
  
  For more fine control you can use a callback. See Callback Codes for the available attributes.

  import sys
  import gurobipy as gp
  from gurobipy import GRB
  
  
  def mycallback(model, where):
  
      if where == GRB.Callback.BARRIER:
          # Barrier callback
          itcnt = model.cbGet(GRB.Callback.BARRIER_ITRCNT)
          primobj = model.cbGet(GRB.Callback.BARRIER_PRIMOBJ)
          dualobj = model.cbGet(GRB.Callback.BARRIER_DUALOBJ)
          priminf = model.cbGet(GRB.Callback.BARRIER_PRIMINF)
          dualinf = model.cbGet(GRB.Callback.BARRIER_DUALINF)
          cmpl = model.cbGet(GRB.Callback.BARRIER_COMPL)
          if abs(primobj - dualobj) <= 1:
              print("Custom gap reached")
              model.terminate()
          print("%d %g %g %g %g %g" % (itcnt, primobj, dualobj, priminf, dualinf, cmpl))
  
  
  if len(sys.argv) < 2:
      print("Usage: callback.py filename")
      sys.exit(0)
  
  
  # Read model from file
  model = gp.read(sys.argv[1])
  model.params.Method = 2 # fix to barrier
  model.optimize(mycallback)

  Cheers, 
  David

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  Ishit Bajpai

  July 21, 2022 06:43 Edited

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  Thanks for your answer.

  I set my difference as 1 and got the desired result.

  Custom gap reached
  
  12 2.94524 2.2359 0.00116249 1.27134e-14 1.57297e-06

  However,I want decision variable's value also.

  objective value :  inf

  Is there any way that i can choose my optimal value to be next greatest integer i.e 3 and get decision variable's value corresponding to it?

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  Ishit Bajpai

  July 25, 2022 07:32 Edited

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  is there any function like BarConvTool which instead of taking relative difference as parameter takes absolute difference as parameter ?
  
  
  

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  David Torres Sanchez

  • Gurobi Staff

  August 01, 2022 10:21

  To retrieve the solution using this callback with a custom stopping criterion, set the Crossover parameter to 0.
  
  Cheers, 
  David

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  Ishit Bajpai

  August 07, 2022 20:36 Edited

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  Thanks for your reply.

  After adding this i am getting my objective value as 0.I am also unable to retrieve decision variable's value.

  Following is the code where mycallback is the function used above.

  m1.params.Crossover = 0   

  m1.optimize(mycallback)

   

   

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  David Torres Sanchez

  • Gurobi Staff

  August 08, 2022 10:19

  Is it because it is terminating at the first iteration with \(\texttt{primobj}\) and \(\texttt{dualobj}\) equal to 0?
  I have checked a fair number of models (the ones in the Gurobi examples data directory) with this approach and it seems to work.
  If so, you can add an extra condition to your termination criteria, to say something like

          if primobj != 0 and dualobj != 0 and abs(primobj - dualobj) <= 1:
              print("Custom gap reached")
              model.terminate()

  Cheers, 
  David

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