paref.pareto_reflections.find_1_pareto_points

Classes

Find1ParetoPoints(dimension_domain, dimension)

Find a Pareto point which is minimal in some specified component

class paref.pareto_reflections.find_1_pareto_points.Find1ParetoPoints(dimension_domain: int, dimension: int, epsilon: float = 0.001)

Bases: MinimizeWeightedNormToUtopia

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.

Examples

# TBA: add

Specify the dimension of the input domain and the component in which the minimum 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 in which the minimum is searched

type dimension:

int

param epsilon:

weight on the other components

type epsilon:

float default 1e-3

property dimension_codomain: int

property dimension_domain: int