funObjZitzlerDebThiele42

PURPOSE ^

% Zitzler-Deb-Thiele N4 2nd objective function

SYNOPSIS ^

function [p,dp]=funObjZitzlerDebThiele42(xx)

DESCRIPTION ^

% Zitzler-Deb-Thiele N4 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 N4 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]=funObjZitzlerDebThiele42(xx)
0025 
0026 %constants
0027 a=91;
0028 b=10;
0029 c=4*pi;
0030 
0031 %responses and derivatives
0032 f1=xx(:,:,1);
0033 %
0034 cx=cos(c*xx(:,:,2:end));
0035 td=xx(:,:,2:end).^2-b*cx;
0036 g=a+sum(td,3);
0037 %
0038 rfg=f1./g;
0039 h=1-sqrt(rfg);
0040 %
0041 p=g.*h;
0042 
0043 if nargout==2
0044     %
0045     df1=zeros(size(xx));
0046     df1(:,:,1)=ones(size(xx,1),size(xx,2));    
0047     %
0048     dg=2*xx+b*c*sin(c*xx);
0049     dg(:,:,1)=0;
0050     %
0051     drfg=(df1.*g-f1.*dg)./g.^2;
0052     %
0053     dh=-drfg.*0.5./sqrt(rfg);
0054     %
0055     dp=dg.*h+g.*dh;
0056 end
0057 end

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