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
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
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)
M = list with which elements are in the first front
F = list with the front of each element
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
Visualization of points in high dimensions with parallel coordinates
Makes it faster.
Solves a minor problem that happened when a point dominated itself
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