  A common goal in evolutionary multi-objective optimization is to find
suitable finite-size approximations of the Pareto front of a given
multi-objective optimization problem. While many multi-objective evolutionary
algorithms have proven to be very efficient in finding good Pareto front
approximations, they may need quite a few resources or may even fail to obtain
optimal or nearly approximations. Hereby, optimality is implicitly defined by
the chosen performance indicator. In this work, we propose a set-based Newton
method for Hausdorff approximations of the Pareto front to be used within
multi-objective evolutionary algorithms. To this end, we first generalize the
previously proposed Newton step for the performance indicator for the treatment
of constrained problems for general reference sets. To approximate the target
Pareto front, we propose a particular strategy for generating the reference set
that utilizes the data gathered by the evolutionary algorithm during its run.
Finally, we show the benefit of the Newton method as a post-processing step on
several benchmark test functions and different base evolutionary algorithms.
