paref.pareto_reflections.find_edge_points#

Classes

FindEdgePoints(dimension_domain, dimension)

Find the edge points of the Pareto front

class paref.pareto_reflections.find_edge_points.FindEdgePoints(dimension_domain: int, dimension: int, epsilon: float = 0.001)[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 to dimensions, the edge points of the Pareto front always exist.

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 in which the minimum is searched.

Examples

# TBA: add

Specify the dimension of the input domain and the component of which the edge point is searched

Warning

The smaller epsilon, the better. However, picking an epsilon too small may lead to an unstable optimization.

param dimension_domain:: dimension of domain (i.e. dimension of target space of blackbox function)
type dimension_domain:: int
param dimension:: component of which the edge point is searched
type dimension:: int
param epsilon:: weight on the component
type epsilon:: float default 1e-3