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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

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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

Comments and Ratings (3)

Baris

Baris (view profile)

Vitor

Vitor (view profile)

It has been very useful for me.
Thanks, Alan!

ilpazzo

It's working fine, I'll give u soon some feedback from my work. Thanks

Updates

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

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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