Calculate Nadir point

[shdotcom]

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]

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.