Model Infeasible by solving multi-objective model

Answered

John Raphy Karippery

October 22, 2021 19:55 Edited

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Hello,
I am solving a multi-objective model using the epsilon constrain method. but my code is not working. after using the epsilon method model become infeasible.  is that possible to use epsilon constrain gurobi? can you check what is an issue in my code? 

# max f1 = X1 <br>

# max f2 = 3 X1 + 4 X2 <br>

# st  X1 <= 20 <br>

#     X2 <= 40 <br>

#     5 X1 + 4 X2 <= 200 <br>

m = Model('power')

x1 = m.addVar(vtype=GRB.CONTINUOUS)

x2 = m.addVar(vtype=GRB.CONTINUOUS)

c1 = m.addConstr(x1<=20)

c2 = m.addConstr(x2<=40)

c3 = m.addConstr(5*x1+4*x2 <= 200)

f1 = m.addVar()

f2 = m.addVar()

c_f1 = m.addConstr(f1==x1)

c_f2 = m.addConstr(f2 == (3*x1)+(4*x2))

o_f1 = m.setObjective(f1,GRB.MAXIMIZE)

#o_f2 = m.setObjective(f2,GRB.MAXIMIZE)

m.update()

m.optimize()

apply epsilon constrain

f2_min = 60

f2_max = 184

e = 0 # parameter value initialize 0 and editable

C_epsilon = m.addConstr(f2 == e)

m.update()

m.optimize() 

n = 4

step = int((f2_max - f2_min) / n)

steps = list(range(int(f2_min),int(f2_max),step)) + [f2_max]

x1_l = []
x2_l = []
for i in steps:

    e = i
    C_epsilon = m.addConstr(f2 == e)
    m.optimize()

    x1_l.append(x1) # add x1 variable value into list by each loop
    
    x2_l.append(x2) # add x2 variable value into list by each loop

print(x1_l,x2_l)

what is wrong with my code. 
for reference model explanation 

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 02:45 Edited

  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 why not try our AI Gurobot?.
• 

  Jaromił Najman

  • Gurobi Staff

  October 25, 2021 09:23

  Hi John,

  By using

  C_epsilon = m.addConstr(f2 == e)

  in the \(\texttt{for}\)-loop, you are adding new constraints, instead of modifying the old one. What you are looking for is

  C_epsilon.RHS = e

  in the \(\texttt{for}\)-loop.

  Please note that for LPs, there are possibly better ways to obtain the Pareto Front than using the \(\epsilon\)-method, e.g., Aneja & Nair 1979, Cohon 1978, Ehrgott 2000.

  Best regards,
  Jaromił

  Best regards,
  Jaromił

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• 

  John Raphy Karippery

  October 25, 2021 16:56

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  Hello Jaromił,
  
  

  Thank you so much for your help and referances.
  all referances you mention are not free so I need to find another way find that referances.

  I have one more question about the lower and upper bounds (f2_min,f2_max ). Here in my code I pre defined value. 

  Is there any simple way to find f2_min and f2_max in gurobi? 
  
  Here I submit code for argument e-constraint. that will help for others:
  
  

  # deactivate all objective 
  # remove C_epsilon = m.addConstr(f2 == e)
  
  
  m.optimize()
  x1_l = []
  x2_l = []
  e=0
  delta = 0.00001
  s = m.addVar(vtype=GRB.CONTINUOUS)
  O_f1 = m.setObjective(f1+(delta*s), GRB.MAXIMIZE)
  C_e = m.addConstr(f2-s == e)
  
  for i in range(160,190,6):
       e = i
       C_e.RHS = e
       m.optimize()
       v=m.getVars()
       x1_l.append(v[0].x)
       x2_l.append(v[1].x)
  
  plt.plot(x1_l,x2_l,'o-.');
  plt.title('efficient Pareto-front');
  plt.grid(True);

  Thank you
  john Karippery

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• 

  Jaromił Najman

  • Gurobi Staff

  October 26, 2021 07:33

  Hi John,

  Is there any simple way to find f2_min and f2_max in gurobi? 

  You can find the f2_min and f2_max values by minimizing and maximizing the underlying model and setting f2 as its objective. So basically change

  o_f1 = m.setObjective(f1,GRB.MAXIMIZE)

  to

  o_f2 = m.setObjective(f2,GRB.MAXIMIZE)
  m.optimize()
  f2_max = m.ObjVal
  o_f2 = m.setObjective(f2,GRB.MINIMIZE)
  m.optimize()
  f2_min = m.ObjVal

  and then proceed with the rest of your code.

  Best regards,
  Jaromił

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