Model ignoring setPWLObj()

Answered

Fabio Ciccarelli

• August 29, 2023 11:16

Hi!

I am trying to build a model having a certain non-convex piecewise linear function as the objective function, related only to a subset of the variables. So, I defined the variables as:

s = model.addVars(var_list, lb = 0., vtype = GRB.CONTINUOUS, name = 's')

 

Then, I defined a subset of var_list, named var_sublist, and introduced the following objective for this subset:

 

for u in var_sublist:

        model.setPWLObj(s[u], [0,1,2], [0,1,1])

 

As you can see, the PWLObj is a linear function with zero intercept and slope equal to 1 for input values less or equal than 1, and then it becomes a constant-1 function. The idea is that this objective function should serve to count the number of strictly positive variables in var_sublist (and to minimize the overall number of them). 

The fact is that my model, when optimizing, is completely ignoring the PWL objective functions. Is there something I made wrong? Note that I did not define other objectives for the rest of the variables not in var_sublist, but even when I did it nothing changed.

 

Thanks for your help. 

Related to

• Piecewise Linear

0

• 

  Eli Towle

  Gurobi Staff

  • August 29, 2023 17:57

  What makes you think Gurobi is ignoring the PWL objective terms? Can you please post a complete, minimal reproducible code example that shows the behavior you describe?

  0
• 

  Fabio Ciccarelli

  • August 30, 2023 09:09

  

  

  

  var_list = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'l', 'm', 'n']
  
  var_sublist = ['d', 'h', 'n']
  
  distance_dict = {('a', 'b') : 10,
  
                   ('b', 'c') : 7,
  
                   ('c', 'd') : -17,
  
                   ('e', 'f') : 8,
  
                   ('f', 'g') : 8,
  
                   ('g', 'h') : -16,
  
                   ('i', 'l') : 4,
  
                   ('l', 'm') : 7,
  
                   ('m', 'n') : -11,
  
                   ('l', 'e') : 0,
  
                   ('l', 'a') : 0,
  
                   ('f', 'a') : 0,}
  
  for var in var_list:
  
          distance_dict[('start', var)] = 0
  
  var_list.insert(0, 'start')
  
  model = gp.Model()
  
  model.Params.LogToConsole = 0
  
  s = model.addVars(var_list, lb = 0, vtype = GRB.CONTINUOUS, name = 's')
  
  for u in var_sublist:
  
          model.setPWLObj(s[u], [0,1,2], [0,1,1])
  
  for (u,v) in distance_dict:
  
          model.addConstr(s[v] - s[u] >= distance_dict[u, v])
  
  model.optimize()
  
  for var in var_sublist:
  
          print(var, s[var].X)
  
  print(f'The optimal o.f. value is equal to: {model.getObjective().getValue()}')
  
  # IT PRINTS 0 EVEN IF WE HAVE MORE THAN A VARIABLE BELONGING TO var_sublist WITH VALUES HIGHER THAN 0

  0
• 

  Fabio Ciccarelli

  • August 30, 2023 09:11

  

  

  

  I think the problem can be related to the way I retrieve the objective value as well, but I did not manage to find on the web a way to retrieve optimal PWL Objective value after optimization. 

   

  Thanks for your help.

  0
• 

  Eli Towle

  Gurobi Staff

  • August 30, 2023 17:23

  If you leave LogToConsole at its default value, Gurobi shows the optimal objective value of the problem is \(2\):

  Gurobi Optimizer version 10.0.2 build v10.0.2rc0 (mac64[arm])
  
  CPU model: Apple M1 Pro
  Thread count: 8 physical cores, 8 logical processors, using up to 8 threads
  
  Optimize a model with 24 rows, 13 columns and 48 nonzeros
  Model fingerprint: 0xaacfb7ec
  Model has 3 piecewise-linear objective terms
  Variable types: 13 continuous, 0 integer (0 binary)
  Coefficient statistics:
    Matrix range     [1e+00, 1e+00]
    Objective range  [0e+00, 0e+00]
    Bounds range     [0e+00, 0e+00]
    RHS range        [4e+00, 2e+01]
    PWLObj x range   [1e+00, 1e+00]
    PWLObj obj range [1e+00, 1e+00]
  Presolve removed 24 rows and 13 columns
  Presolve time: 0.00s
  Presolve: All rows and columns removed
  
  Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
  Thread count was 1 (of 8 available processors)
  
  Solution count 1: 2 
  
  Optimal solution found (tolerance 1.00e-04)
  Best objective 2.000000000000e+00, best bound 2.000000000000e+00, gap 0.0000%

  Unfortunately, Model.getObjective() only includes the linear and quadratic objective terms, not the piecewise-linear objective terms. You can retrieve the optimal objective value of the model by querying the ObjVal model attribute:

  model.ObjVal

  0
• 

  Fabio Ciccarelli

  • August 31, 2023 11:19

  

  

  

  Thank you so much for your time and kindness!

  0

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