paref.pareto_reflections.find_1_pareto_points

Classes

Find1ParetoPoints(dimension, blackbox_function)

Find a Pareto point which is minimal in some specified component

class paref.pareto_reflections.find_1_pareto_points.Find1ParetoPoints(dimension: int, blackbox_function: BlackboxFunction)

Bases: MinGParetoReflection

Find a Pareto point which is minimal in some specified component

When to use

This Pareto reflection should be used if a Pareto point is desired which lie on the boundary of the Pareto front, i.e. are minimal in one component.

Note

In to dimensions, the edge points of the Pareto front are given by the boundary of the Pareto front. I.p. in two dimensions, this Pareto reflection searches for the edge points of the Pareto front.

What it does

The Pareto points of this map are the ones which minimize the weighted sum where one component is given much more weight than the others.

Mathematical formula

\[p(x) = \sum_{i=1,...,n,i\neq j}\epsilon x_{i}+ x_j\]

where \(j\) is the component in which the minimum is searched.

param dimension:

component in which the minimum is searched

param blackbox_function:

blackbox function to which this reflection is applied

property g