paref.pareto_reflections.find_edge_points#

Classes

FindEdgePoints(dimension, blackbox_function)

Find the edge points of the Pareto front

class paref.pareto_reflections.find_edge_points.FindEdgePoints(dimension: int, blackbox_function: BlackboxFunction)[source]#

Find the edge points of the Pareto front

Warning

This Pareto reflection assumes that there exist edge points

When to use#

This Pareto reflection should be used if the edge points of the Pareto front are searched.

Note

In two dimensions, the edge points of the Pareto correspond to the Pareto points which are minimal in one component, i.e. to the one Pareto points.

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

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

where \(j\) is the component to which the edge corresponds.

param dimension:: component to which the edge corresponds
param blackbox_function:: blackbox function to which this reflection is applied