# Pareto Fronts according to dominance relation

Version 1.5.0.0 (7.51 KB) by
Finds the fronts from a set of n-dimensional points according to a certain dominance relation
Updated 29 Oct 2012

PARETOFRONTS from a set of points x with a certain dominance relation dom

[M,F] = PARETOFRONTS(x,objective,dom,make_plot,parameter) can find and/or
plot the first or all the pareto fronts according to one of 7 relations
of dominance among points of any dimension

Inputs:
x = table with point in format (N, M) where N is the number of
points and M is their dimension

objective = array specifying if we want to minimize (0) or maximize (1)
each dimension (default = 1)

dom = string or number with a dominace relation (default = pareto
dominance)
possible values: 1 - 'pareto'
2 - 'lexicographic'
3 - 'extrema'
4 - 'maxdom'
5 - 'cone'
6 - 'epsilon'
7 - 'lorenz'

make_plot = 0, 1 or 2, plots the points and their fronts

parameter = available for 'lexicographic' (rank of importance between objectives of length M)
'extrema' (weight vector for each objective of length M)
'epsilon' (epsilon > 0, resolution vector of length M or 1)
'cone' (inclination value lambda (default value is 0.2) of length 1)

Outputs:
M = list with which elements are in the first front
F = list with the front of each element

Examples:

members = paretofronts(randn(100,3),[1,1,1],1,1);

[members, fronts] = paretofronts(randn(100,2),[0,0],1,1);

x = randn(50,2); for i=1:7 subplot(2,4,i); paretofronts(x,[0,0],i,1); end

### Cite As

Alan de Freitas (2024). Pareto Fronts according to dominance relation (https://www.mathworks.com/matlabcentral/fileexchange/37080-pareto-fronts-according-to-dominance-relation), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2011a
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Categories
Find more on Multiobjective Optimization in Help Center and MATLAB Answers

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

#### ParetoFronts/

Version Published Release Notes
1.5.0.0

Visualization of points in high dimensions with parallel coordinates

1.3.0.0

Makes it faster.

1.2.0.0

Solves a minor problem that happened when a point dominated itself

1.0.0.0