  Some quality indicators have been proposed for benchmarking preference-based
evolutionary multi-objective optimization algorithms using a reference point.
Although a systematic review and analysis of the quality indicators are helpful
for both benchmarking and practical decision-making, neither has been
conducted. In this context, first, this paper reviews existing regions of
interest and quality indicators for preference-based evolutionary
multi-objective optimization using the reference point. We point out that each
quality indicator was designed for a different region of interest. Then, this
paper investigates the properties of the quality indicators. We demonstrate
that an achievement scalarizing function value is not always consistent with
the distance from a solution to the reference point in the objective space. We
observe that the regions of interest can be significantly different depending
on the position of the reference point and the shape of the Pareto front. We
identify undesirable properties of some quality indicators. We also show that
the ranking of preference-based evolutionary multi-objective optimization
algorithms depends on the choice of quality indicators.
