paref.pareto_reflections.fill_gap_2d

Classes

FillGap2D(point_1, point_2, utopia_point[, ...])

Fill the gap between two to be specified points in two dimensions

class paref.pareto_reflections.fill_gap_2d.FillGap2D(point_1: ndarray, point_2: ndarray, utopia_point: ndarray, potency: int = 6)

Bases: MinimizeWeightedNormToUtopia

Fill the gap between two to be specified points in two dimensions

Warning

Although this Pareto reflection theoretically closes every gap, if the utopia point is far away from the gap, algorithms based on this Pareto reflection tend to be numerically unstable. It is recommended to choose an utopia point which is as close to the gap as possible.

When to use

This Pareto reflection should be used if a Pareto point is desired which lies between two specified points

Note

This function works best if the two points are Pareto optimal.

What it does

The Pareto points of this map are the ones which sit in the middle of the two given points (provided that such a point exists).

Mathematical formula

\[TBA\]

Examples

TBA: Add

Specify the gap and some utopia point

param point_1:

first point defining the gap

type point_1:

np.ndarray

param point_2:

second point defining the gap

type point_2:

np.ndarray

param utopia_point:

utopia point

type utopia_point:

np.ndarray

param potency:

potency of underlying weighted norm

type potency:

int default 6

property dimension_codomain: int

property dimension_domain: int