Calculates the Coverage metric [1] (also known as the C-metric) given two sets of points.
cov(x, y, ...)
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Coverage value.
Given two (approximation) sets \(X = \{x_1, \ldots, x_{|X|}\}\) and \(Y = \{y_1, \ldots, y_{|Y|}\}\) this indidcator calculates the fraction of points from \(Y\) which are dominated by at least one point \(x \in X\). Formally, it is defined as: $$ C(X, Y) = \frac{|\{y \in Y \mid \exists x \in X,\, x \preceq y\}|}{|Y|}. $$ It holds that \(C(X, Y) \in [0,1]\). Note that in general \(C(X, Y) \neq 1 - C(Y, X)\).
Keep in mind that this function assumes all objectives to be minimized. In case at least one objective is to be maximized, the data needs to be transformed accordingly in advance.
[1] E. Zitzler, Evolutionary algorithms for multiobjective optimization: Methods and applications, Ph.D. thesis, Swiss Federal Institute of Technology Zurich (1999).