% Penalty 1 function L. LAURENT -- 21/03/2017 -- luc.laurent@lecnam.net
0001 %% Penalty 1 function 0002 %L. LAURENT -- 21/03/2017 -- 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 % 0025 %global minimum : f(x)=0 for xi=-1 0026 % 0027 %Design space: -50<xi<50 0028 % 0029 0030 0031 0032 function [p,dp]=funPenalty1(xx) 0033 %constants 0034 a=pi/30; 0035 b=10; 0036 c=pi; 0037 d=1; 0038 e=100; 0039 f=4; 0040 0041 %evaluation and derivatives 0042 y=d+1/f*(xx+d); 0043 % 0044 pa=sin(c*y(:,:,1)); 0045 pb=y(:,:,1:end-1)-d; 0046 sc=sin(c*y(:,:,2:end)); 0047 pc=d+b*sc.^2; 0048 pd=y(:,:,end)-d; 0049 % 0050 u=zeros(size(xx)); 0051 IXb=abs(xx)>b; 0052 u(IXb)=e*(abs(xx(IXb))-b).^f; 0053 % 0054 p=a*(b*pa.^2+sum(pb.^2.*pc,3)+pd.^2)+sum(u,3); 0055 %p=a*pd.^2; 0056 %keyboard 0057 % 0058 if nargout==2 0059 % 0060 dp=zeros(size(xx)); 0061 % 0062 du=zeros(size(xx)); 0063 du(IXb)=f*e*sign(xx(IXb)).*(abs(xx(IXb))-b).^(f-1); 0064 % 0065 ppa=cos(c*y(:,:,1)); 0066 cc=cos(c*y(:,:,2:end)); 0067 % 0068 dp(:,:,1)=2*a*b*c/f.*pa.*ppa... 0069 +2*a/f*pb(:,:,1).*pc(:,:,1)... 0070 +du(:,:,1); 0071 dp(:,:,end)=2*a*b*c/f.*sc(:,:,end).*cc(:,:,end).*pb(:,:,end).^2 ... 0072 +2*a/f*pd... 0073 +du(:,:,end); 0074 dp(:,:,2:end-1)=2*a*b*c/f.*sc(:,:,1:end-1).*cc(:,:,1:end-1).*pb(:,:,1:end-1).^2 ... 0075 +2*a/f*pb(:,:,2:end).*pc(:,:,2:end)... 0076 +du(:,:,2:end-1); 0077 end