Adding constraints only if a certain condition is verified

Answered

Maria Laura Santoni

• November 20, 2023 00:44

Hi everyone,

I am trying to model a problem on Gurobi Python. I have n binary variables and each couple has assigned a fixed number that I load from outside. 

A constraint that the problem should have is that if var_i =1 and var_j =1 then dist_ij>= min_dist

where dist_ij is the fixed number (float) that is assigned to the couple with the indexes i and j and min_dist is a fixed number that I decide.

Thanks a lot!

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• 

  Simranjit Kaur

  Gurobi Staff

  • November 20, 2023 05:39

  Hi Maria,

  It seems you are trying to find the minimum of the dist_ij when the fixed number (loaded from outside) assigned to both i and j is 1. In this case, the min_dist calculation can simply be done in Python (no need to define any variables or constraints):

  min_dist = min( dist_ij for i in I for j in I if num_i = 1 and num_j = 1)

  where num_i is the fixed number assigned to i. Please note here I am assuming that dist_ij is a known fixed value for every pair of i and j.

  Best regards,
  Simran

  0
• 

  Maria Laura Santoni

  • November 20, 2023 05:48

  

  

  Hi Simran,

  This is my current code:

  from gurobipy import Model, GRB, quicksum

  import numpy as np

  
  
  

  # Carica i pesi da un file txt (10000 pesi)

  weights = np.loadtxt('15_0_2_10000_5_-5_5_1000_sample_values.txt', usecols=[0], skiprows=1)

  
  

  # Carica le distanze da un file txt (10000 righe e 10000 colonne)

  distances = np.loadtxt('distances.txt')

  
  

  # Creazione del modello

  model = Model()

  
  

  # Crea le variabili binarie

  num_var = len(weights)

  var = model.addVars(num_var, vtype=GRB.BINARY, name="variable")

  #distanza_vars = model.addVars([(i, j) for i in range(num_var) for j in range(i + 1, num_var)], vtype=GRB.INTEGER, name="distanza_var")

  
  

  # Constants

  # M is chosen to be as small as possible given the bounds on x and y

  # eps = 0.0001

  # M = 2 + eps

  # Crea il vincolo per la distanza tra i punti

  min_dist = 3  # Specifica il valore minimo di distanza

  dist_var = model.addVars(num_var, num_var, vtype=GRB.INTEGER, name='dist_var')

  for i in range(num_var):

      for j in range(i + 1, num_var):

          model.addConstr(dist_var[i,j] == var[i] + var[j])

          model.addConstr((dist_var[i,j] == 2) >> (distances[i,j]>=min_dist))

  # Crea il vincolo per la somma delle variabili

  model.addConstr(var.sum() == 5, "sum_constraint")

  # Crea la funzione obiettivo utilizzando le distanze

  # Definisci la funzione obiettivo

  objective = quicksum(var[i] * weights[i] for i in range(num_var))

  model.setObjective(objective, GRB.MINIMIZE)

  
  

  # Ottimizza il modello

  model.optimize()

  
  

  # Stampa i risultati

  if model.status == GRB.OPTIMAL:

      results= f"Optimal value: {model.objVal}\nOptimal solution: {[var[i].x for i in range(num_var)]}"

      # Salva i risultati in un file

      with open('results_d3_f15.txt', 'w') as file:

          file.write(results)

  else:

      print("The problem does not have a solution.")

   

   

   

   

  ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

   

  I am trying to put some constraints: if var_i and var_j are both equal to 1 then d_ij has to be bigger or equal to min_dist. I already know d_ij and min_dist to (It is a threshold that I fix before).

   

  with this code, I got the error:

  raceback (most recent call last): File "/dss/dsshome1/lxc0D/ge89yen2/Gurobi/main3.py", line 29, in <module> model.addConstr((dist_var[i,j] == 2) >> (distances[i,j]>=min_dist)) File "src/gurobipy/model.pxi", line 3591, in gurobipy.Model.addConstr File "src/gurobipy/model.pxi", line 4670, in gurobipy.Model.addGenConstrIndicator TypeError: unsupported operand type(s) for -=: 'NoneType' and 'flo

  0
• 

  Michel Soares

  • November 20, 2023 13:05

  

  

  Hi Maria,

  I believe var_i =1 and var_j =1 then dist_ij>= min_dist could be modelled as:

  dist_ij >= (var_i * var_j  * min_dist)

  That would make your model quadratic, but it should yield the desired result. I believe this would be the constraint, and I encourage you to read the documentation for quadratic constraint:

  model.addQConstr(dist_var[i,j] >= var[j] * var[j] * min_dist)

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• 

  Simranjit Kaur

  Gurobi Staff

  • November 21, 2023 00:32

  Hi Maria,

  Thanks for sharing your code. Since var_i and var_j are decision variables in the model that are not known a priori, the suggestion in my previous comment will not work.

  The condition
               "If var_i =1 and var_j =1, then dist_ij>= min_dist"
  is equivalent to saying
         " If dist_ij < min_dist, then at least one of var_i or var_j must be zero".

  Since distances[i,j] and min_dist are inputs to your model, the above condition can be modelled using linear constraints as follows:

  if distances[i,j] < min_dist:
      model.addConstr(var[i] +var[j] <= 1)

  Best regards,
  Simran

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