% Zitzler-Deb-Thiele N4 2nd objective function L. LAURENT -- 09/05/2018 -- luc.laurent@lecnam.net
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