Overall (Pareto) Spread

Source: R/moo_os.R

Calculates the Overall (Pareto-) Spread multi-objective performance indicator for a point set x.

os(x, np = NULL, ip = NULL, ...)

Arguments

x

[matrix]
Numeric matrix of points (each colum contains one point).
np

[numeric]
Nadir point or approximtion of it.
ip

[numeric]
Ideal point or approximtion of it.
...

[any]
Not used.

Value

Single numeric indicator value.

Details

A simple multi-objective performance indicator proposed in [1]. Given a point set \(X = \{x_1, \ldots, x_{|X|}\}\) of \(m\) objectives, the ideal point \(I\) (or an approximation thereof) and the nadir point \(N\) (or a approximation) it is defined as $$ OS(X) = \prod_{i=1}^{m} \frac{\max_{x \in X} x_i - \min_{x \in X} x_i}{N_i - I_i}. $$ This indicator only captures the extend of the Pareto-front approximation.

References

[1] J. Wu, S. Azarm, Metrics for quality assessment of a multiobjective design optimization solution set, Journal of Mechanical Design 123 (1) (2001) 18–25.

See also

Other multi-objective performance indicators: cov(), df_get_indicators(), eps(), gd(), hv(), r1(), rse()