Asked by Sotirios
on 26 Dec 2013

Is it possible to generate surface pareto front for 3 objective functions and plot it? My actual question is that when we have two objectives, the Pareto front is a line in 2D space and when we have three objectives the Pareto front is a surface in 3d space. How we can obtain that surface?

Answer by Alan Weiss
on 26 Dec 2013

Accepted Answer

Sure.

function f = simple_multiobj2(x,a,b,c)

x = x(:); a = a(:); b = b(:); c = c(:); % all column vectors

f(1) = sqrt(1+norm(x-a)^2);

f(2) = 0.5*sqrt(1+norm(x-b)^2) + 2;

f(3) = 0.25*sqrt(1+norm(x-c)^2) - 4;

Then run this:

a = zeros(2,1);

b = [2;1];

c = [3;-.5];

fun = @(u)simple_multiobj2(u,a,b,c);

[x,f,ef] = gamultiobj(fun,2)

scatter3(f(:,1),f(:,2),f(:,3),'k.');

If you want to plot an interpolated surface or mesh, use scatteredInterpolant.

Alan Weiss

MATLAB mathematical toolbox documentation

Sotirios
on 26 Dec 2013

Alan Weiss
on 27 Dec 2013

F = scatteredInterpolant(f(:,1),f(:,2),f(:,3),'linear','none');

sgr = min(f(:,1)):.01:max(f(:,1));

ygr = min(f(:,2)):.01:max(f(:,2));

[XX,YY] = meshgrid(sgr,ygr);

ZZ = F(XX,YY);

surf(XX,YY,ZZ,'LineStyle','none')

The 'none' argument in scatteredInterpolant removes any extrapolated points, so you just se the true extent of the calculated surface, assuming that linear interpolation shows the truth.

If this sufficiently answers your question, please accept the answer.

Alan Weiss

MATLAB mathematical toolbox documentation

Tarek Salem
on 18 Aug 2014

please i i need to plot 4D function, because the algorithm optimize 4 functions at a time

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