dominates: Dominance relation checks
In jakobbossek/ecr3vis: Evolutionary Computation in R - Version 3

Description Usage Arguments Details Value See Also Examples

Check if a vector dominates another (dominates or does_dominate) or is dominated by another (is_dominated). There are corresponding infix operators dominates and is_dominated.

dominates(x, y)

does_dominate(x, y)

is_dominated(x, y)

x %dominates% y

x %is_dominated% y

`x`	[`numeric`] First vector.
`y`	[`numeric`] Second vector.

Given two vectors x,y \in R^m we say that x dominates y, denoted as x \preceq y if and only if

x_i ≤q y_i \, \forall i \in \{1, …, m\}

and

\exists j \in \{1, …, m\}: x_i < y_i.

Informally, x dominates y if x is no worse than y in all components and x is strictly better than y in at least one component. Note that this definition focuses on minimization of all objectives. This is no restriction since the maximization of some function is equivalent to the minimization of its negative counterpart.

Single logical value.

Other Pareto-dominance checks: dominated(), set_dominates(), which_dominated()

Other multi-objective tools: dominated(), set_dominates(), which_dominated()

dominates(c(2, 3), c(4, 5))
dominates(c(2, 3), c(2, 3))
is_dominated(c(2, 3), c(4, 5))
is_dominated(c(4, 5), c(2, 3))
c(1, 2, 3) %dominates% c(4, 5, 6)
c(1, 2, 3) %is_dominated% c(4, 5, 6)