65 research outputs found
Investigating Normalization in Preference-based Evolutionary Multi-objective Optimization Using a Reference Point
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
Quality Indicators for Preference-based Evolutionary Multi-objective Optimization Using a Reference Point: A Review and Analysis
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
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