How do I obtain Pareto optimal solutions in Gurobi?

Answered

Sagnik Basumallik

February 27, 2020 23:42 Edited

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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?

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 03:17 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?.
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  Yuriy Zinchenko

  • Gurobi Staff

  February 28, 2020 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.

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  Sagnik Basumallik

  February 28, 2020 01:18 Edited

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  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?

   

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  Yuriy Zinchenko

  • Gurobi Staff

  March 04, 2020 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.

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  Sagnik Basumallik

  March 04, 2020 18:12

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

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  Pengfei Su

  May 09, 2022 20:50

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  Hi Sagnik,

  May I know how you solve this problem?

  Many thanks!

  Nick

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