How do I obtain Pareto optimal solutions in Gurobi?

回答済み

Sagnik Basumallik

2020年02月27日 23:42 編集済み

• 
• 
• 

Currently, I am solving a MOOP in Gurobi. The first way is the linearly blended method.

m.setObjective(obj1+obj2+obj3)

Next, I have re-write n-1 objectives using the ε-constraint method,

m.addConstr(obj2 <= ε1)

m.addConstr(obj3 <= ε2)

m.setObjective(obj1)

Next, using (a) hierarchical method, how can I generate Pareto optimal solutions?

m.setObjectiveN(obj1, index = 1, priority = 4, abstol=5.0)
m.setObjectiveN(obj2, index = 2, priority = 3, abstol=4.0)

m.setObjectiveN(obj3, index = 3, priority = 2, abstol=0.0)

 

How do I generate multiple Pareto optimal solutions to obtain a Pareto front?

0

• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 03:17 編集済み

  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?.
• 

  Yuriy Zinchenko

  • Gurobi Staff

  2020年02月28日 01:11

  Hello Sagnik,

  I am not quite sure I understand your question, can you possibly paraphrase?

  Hierarchical method is very similar to what you have described as \epsilon method, expect for the constraint will be imposed on the lower-priority objectives not deviating much from an earlier achieved optimum.  More details can be found here,

  https://www.gurobi.com/documentation/9.0/refman/working_with_multiple_obje.html

  Hope this helps.

  0
• 

  Sagnik Basumallik

  2020年02月28日 01:18 編集済み

  • 
  • 
  • 

  Let us say we have the following:

  m.setObjective(w1*obj1+w2*obj2+w3*obj3)

  or

  m.setObjectiveN(obj1, index = 1, priority = 4, abstol=5.0)

  m.setObjectiveN(obj2, index = 2, priority = 3, abstol=4.0)

  m.setObjectiveN(obj3, index = 3, priority = 2, abstol=0.0)

  Is there a way to generate enough Pareto Optimal solutions to approximate the Pareto front?

   

  0
• 

  Yuriy Zinchenko

  • Gurobi Staff

  2020年03月04日 02:08

  To approximate the Pareto frontier you may want to get more sample points in that set.  Having said that, both the weighted and the hierarchical approach will give you points on the frontier.

   

  Hope this helps.

  0
• 

  Sagnik Basumallik

  2020年03月04日 18:12

  • 
  • 
  • 

  Thank you Dr. Yuriy Zinchenko. I did figure this out later after reading "multi-objective optimization in theory and practice: classical methods 1"

  0
• 

  Pengfei Su

  2022年05月09日 20:50

  • 
  • 

  Hi Sagnik,

  May I know how you solve this problem?

  Many thanks!

  Nick

  0

投稿コメントは受け付けていません。