Hierarchical method for multiobjective optimization: implementation

[Gustavo Aragón]

Dear all,

I am using Gurobi to solve a multiobjective optimization problem. I see that the blended method corresponds to the weighted sum method, I assume this is how it is implemented. I am wondering how exactly is the hierarchical method implemented? I thought this would be the epsilon-constraint method, but from the general information on Gurobi's website about the way it works, it seems that the optimization is "nested", meaning that it seems to run for each objective individually with limitations on the objective function space based on the previous optimization. But the epsilon-constraint method directly transforms all secondary objective functions to constraints. So, from my point of view, the hierarchical method probably does not correspond to the epsilon-constrained method, do I see this correctly?

Best regards,
Gustavo Aragon

[Daniel Espinoza]

Hi Gustavo,

In essence, the hierarchical approach is an epsilon-constrained method, with an extra global preprocessing step.

At each step, we would add the previous objective function (and degradation) as a constraint, and move on the next hierarchical objective.

Best,

Daniel