  Normalization of objectives plays a crucial role in evolutionary
multi-objective optimization (EMO) to handle objective functions with different
scales, which can be found in real-world problems. Although the effect of
normalization methods on the performance of EMO algorithms has been
investigated in the literature, that of preference-based EMO (PBEMO) algorithms
is poorly understood. Since PBEMO aims to approximate a region of interest, its
population generally does not cover the Pareto front in the objective space.
This property may make normalization of objectives in PBEMO difficult. This
paper investigates the effectiveness of three normalization methods in three
representative PBEMO algorithms. We present a bounded archive-based method for
approximating the nadir point. First, we demonstrate that the normalization
methods in PBEMO perform significantly worse than that in conventional EMO in
terms of approximating the ideal point, nadir point, and range of the PF. Then,
we show that PBEMO requires normalization of objectives on problems with
differently scaled objectives. Our results show that there is no clear "best
normalization method" in PBEMO, but an external archive-based method performs
relatively well.
