Multi Objective

Ongoing

Alexandra Baldus

• February 19, 2024 17:10

Hello,

I am trying to solve a multi objective function problem. This is my code:

Z1 = quicksum([yps[p,s] * auftraege['Profit'][p] for p in range(P) for s in range(S)])
Z2 = -quicksum([yps[p,s] * auftraege[f'M{s+1}Energie'][p] for p in range(P) for s in range(S)])
Z3 = -quicksum([yps[p,s] * auftraege[f'M{s+1}Cost'][p] for p in range(P) for s in range(S)])

# Setze die Zielfunktionen
model.setObjectiveN(Z1, index=0, priority=1, name="Z1")
model.setObjectiveN(Z2, index=1, priority=2, name="Z2")
model.setObjectiveN(Z3, index=2, priority=3, name="Z3")

model.optimize()

if model.status == GRB.INFEASIBLE or model.status == GRB.UNBOUNDED:
    print("Problem infeasible oder unbounded.")
else:
    Z_values=[model.objVal for t in range(3)]
    print("Optimal values:", Z_values)  

    total_objective_value = sum(Z_values)
    print(f"Total value of objective function: {total_objective_value}")

In my code, Z1 should be maximized, and Z2 and Z3 minimized (given by signs). Lexicographic optimization should maximize the entire model. Currently, my solution value for all Z is identical. Where is my mistake? Also, why does Gurobi optimize Z3 first, then Z2, then Z1, even though I have set priorities?

 

Related to

• Multiple Objectives

0

• 

  Ronald van der Velden

  Gurobi Staff

  • February 19, 2024 19:41

  Hi Alexandra,

  • We optimize highest priority first, so that's why Z3 is solved first in your case.
  • When you iterate over range(3) to retrieve the objective values, you'll always get the same objective value since you don't request the objective value for a specific objective. While you iterate, you should set the ObjNumber model attribute to t and then request the ObjNVal attribute. See this example for some more information.

  Hope that helps!

  Kind regards,
  Ronald

  0
• 

  Alexandra Baldus

  • February 23, 2024 16:27

  

  

  Hi Ronald,

  thank you very much for your help!

  Is this the right way to implement?

  model.setObjectiveN(Z1, index=0, priority=2, name="Z1")
  model.setObjectiveN(Z2, index=1, priority=1, name="Z2")
  model.setObjectiveN(Z3, index=2, priority=0, name="Z3")

  
  model.optimize()

  Z_values = []

  for t in range(3):
      model.setParam(GRB.Param.ObjNumber, t)
      Z_values.append(model.ObjNVal)

  if model.status == GRB.INFEASIBLE or model.status == GRB.UNBOUNDED:
      print("Das Problem ist unlösbar oder unbeschränkt.")
  else:
      print("Optimale Zielfunktionswerte:", Z_values)

      total_objective_value = sum(Z_values)
      print(f"Gesamtwert der Zielfunktion: {total_objective_value}")

  Unfortunately, I now get the value 0 as the optimal solution. Am I missing something?

  King regards, 

  Alexandra 

  0

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