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.

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?

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.

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