MILP vs Pareto

[Wafa Lakhdhar]

Hi,

Please, i want to know the difference between MILP technique and Pareto optimal method.
Thank you in advance,


Best regards,
Wafa

[Tobias Achterberg]

Regular mixed integer linear programming (MILP) is about finding one optimal
solution (a problem instance may have multiple optimal solutions) for a given
optimization problem with linear objective function, linear constraints, and
some variables being restricted to take integer values.

Pareto optimization is about models with multiple objective functions. One seeks
to find the so-called "Pareto frontier". A feasible solution x is member of the
Pareto frontier if there is no feasible solution y, so that y is strictly better
than x in some objective function and at least as good as x for all other
objective functions.

The concept of Pareto optimization (or, more general, of multi-objective
optimization) can be applied to any optimization problem. Of course, you can
also look at the special case of Pareto optimization for MILPs.

Gurobi supports multi-objective optimization for MILPs, but not Pareto
optimization. It only supports weighted and hierarchical objective functions.


Regards,

Tobias

[Wafa Lakhdhar]

Many thanks for your reply Tobias.