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fcampelo / DEMO

Differential Evolution for Multiobjective Optimization and its variants
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Calculate Nadir point #5

Open shdotcom opened 5 years ago

shdotcom commented 5 years ago

Hi, Dear Felipe Campelo,

Would you please explain how did you get these formulations to calculate Nadir point in In DTLZ5, 6 and Nadir, faux and zstar in DTLZ7?

case {'dtlz5', 'dtlz6'}
        zstar = zeros(M,1);
        znad = (1/sqrt(2)) .^ ([M-2, M-2:-1:0]');

case 'dtlz7'
        xaux = 0.85940;
        faux = 2*(M - (M-1)*xaux/2*(1 + sin(3*pi*xaux)));
        zstar = [zeros(M-1,1); faux];
        znad = [xaux(ones(M-1,1)); 2*M];

And how did you get this value xaux = 0.85940; in DTLZ7?

Thank you

fillipe-gsm commented 5 years ago

Hi, shdotcom,

I believe this question was properly answered during our private conversations.

For other users with the same inquiry, I moved the DTLZ code to a separate repository: https://github.com/fillipe-gsm/dtlz-test-functions and added a pdf file inside the docs folder explaining the derivation of these equations.

With that said, I suppose this issue can be closed.