Multi objective optimization - non dominant solution

Hi Jaromil,

I had a question regarding a bi objective problem that I am solving. I have two objectives: objective 1 minimizes total travel time and objective 2 minimizes total unmet demand. I am using the reltol on objective 1 and allowing to objective 2 to degrade the value by giving a specified relative amount. I am setting the reltol values as 1%,2%,3%,4% and 5% to set the amount for relative degradation. Since the dataset for my problem is very large, I do not want to exhaustively find all optimal solution. I am only interested in finding the Pareto Frontier, for which I am finding using Reltol.

My question was - Are all these value given by Gurobi, the non-dominant solutions for this bi-objective function? When I plot the values in a scatter plot, it does form an inverse relationship graph( as shown in the below image) so it does look like a pareto frontier for this optimization.

I also wanted to added that I am solving the bi objective problem by hierarchical lexicographic method. The priority of objective 1 is 2 and the priority of objective 2 is 1. Here is the piece of code for your reference :


m.setObjectiveN(Obj1, index = 0, priority = 2, name = "Obj1", reltol = 0.01)
m.setObjectiveN(Obj2, index = 1, priority = 1, name = "Obj2")

Thanks,

Purnima

Multi objective optimization - non dominant solution

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