funObjZitzlerDebThiele62

PURPOSE ^

% Zitzler-Deb-Thiele N6 2nd objective function

SYNOPSIS ^

function [p,dp]=funObjZitzlerDebThiele62(xx)

DESCRIPTION ^

% Zitzler-Deb-Thiele N6 2nd objective function
L. LAURENT -- 09/05/2018 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Zitzler-Deb-Thiele N6 2nd objective function
0002 %L. LAURENT -- 09/05/2018 -- luc.laurent@lecnam.net
0003 
0004 % sources available here:
0005 % https://bitbucket.org/luclaurent/optigtest/
0006 % https://github.com/luclaurent/optigtest/
0007 
0008 % optiGTest - set of testing functions    A toolbox to easy manipulate functions.
0009 % Copyright (C) 2017  Luc LAURENT <luc.laurent@lecnam.net>
0010 %
0011 % This program is free software: you can redistribute it and/or modify
0012 % it under the terms of the GNU General Public License as published by
0013 % the Free Software Foundation, either version 3 of the License, or
0014 % (at your option) any later version.
0015 %
0016 % This program is distributed in the hope that it will be useful,
0017 % but WITHOUT ANY WARRANTY; without even the implied warranty of
0018 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0019 % GNU General Public License for more details.
0020 %
0021 % You should have received a copy of the GNU General Public License
0022 % along with this program.  If not, see <http://www.gnu.org/licenses/>.
0023 
0024 function [p,dp]=funObjZitzlerDebThiele62(xx)
0025 
0026 %constants
0027 a=9;
0028 b=0.25;
0029 
0030 %responses and derivatives
0031 if nargout==2
0032     [f1,df1]=funObjZitzlerDebThiele61(xx);
0033 else
0034     f1=funObjZitzlerDebThiele61(xx);
0035 end
0036 %
0037 td=sum(xx(:,:,2:end),3);
0038 g=1+a/a^b*td.^b;
0039 %
0040 rfg=f1./g;
0041 h=1-rfg.^2;
0042 %
0043 p=g.*h;
0044 
0045 if nargout==2 
0046     %
0047     dg=a/a^b*b*ones(size(xx)).*td.^(b-1);
0048     dg(:,:,1)=0;
0049     %
0050     dh=-(df1.*g-f1.*dg)./g.^2.*2.*rfg;
0051     %
0052     dp=dg.*h+g.*dh;
0053 end
0054 end

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