os: Overall (Pareto) Spread
In jakobbossek/ecr3vis: Evolutionary Computation in R - Version 3

Description Usage Arguments Details Value References See Also

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

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

`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.

A simple multi-objective performance indicator proposed in [1]. Given a point set X = \{x_1, …, 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) = ∏_{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.

Single numeric indicator value.

[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.

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