paref.pareto_reflections.restrict_by_point

Classes

RestrictByPoint(nadir, restricting_point)

Restrict the Pareto points in the target space by demanding each component to be lower than some value

class paref.pareto_reflections.restrict_by_point.RestrictByPoint(nadir: ndarray, restricting_point: ndarray)

Bases: ParetoReflection

Restrict the Pareto points in the target space by demanding each component to be lower than some value

When to use

This Pareto reflection should be used if Pareto points are desired which dominate a certain point, i.e. when every component of a found Pareto points \(x\) must satisfy \(x_i\le r_i\) for some \(r_i \in \mathbb{R}\).

What it does

The Pareto points of this map are all the Pareto points which dominate that point.

Mathematical formula

Denote by d the point which should be dominated and n some nadir (i.e. n dominated by all points). Then,

\[p(x) = x\]

if x dominates or is equal to d and

\[p(x) = n\]

else.

Examples

Define the nadir and the point which should be dominated

>>> import numpy as np
>>> nadir, restricting_point = np.array([3,7]),np.zeros(2)

Initialize the Restricting

>>> pareto_reflection = RestrictByPoint(nadir=nadir,restricting_point=restricting_point)

Calling it to (1,1), i.e. calculating

\[p(1,1)=(3,7)\]

yields:

>>> pareto_reflection(np.ones(2))
array([3, 7])

Specify the nadir and the to be dominated point

param nadir:

param np.ndarray:

nadir (dominated by all points) stored in 1 dimensional array of length n

param restricting_point:

param np.ndarray:

point to be dominated stored in 1 dimensional array of length n

__call__(x: ndarray) → ndarray

Calculate the RestrictByPoint function

Parameters:

• x –

• np.ndarray – input vector stored in 1 dimensional array of length n

Returns:

value of the restricting function

Return type:

float

property dimension_codomain: int

property dimension_domain: int