% Ackley's function 1 L. LAURENT -- 31/10/2016 -- luc.laurent@lecnam.net
0001 %% Ackley's function 1 0002 %L. LAURENT -- 31/10/2016 -- 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 %numerous local minima 0026 %1 global minimum : x=(0,0,...,0) >> f(x)=0 0027 % 0028 %design space -35<xi<35 (small range -2<xi<2) 0029 0030 function [p,dp]=funAckley1(xx) 0031 0032 %constants 0033 a=20; 0034 b=0.02; 0035 c=2*pi; 0036 d=exp(1); 0037 0038 %number of variables 0039 nbvar=size(xx,3); 0040 0041 %responses and derivatives 0042 normP=sqrt(sum(xx.^2,3)); 0043 ex1=exp(-b*normP/sqrt(nbvar)); 0044 sco=sum(cos(c*xx),3); 0045 ex2=exp(1/nbvar*sco); 0046 p=-a*ex1-ex2+a+d; 0047 0048 if nargout==2 0049 dp=a*b*1/sqrt(nbvar)*xx./normP.*ex1+c/nbvar*sin(c*xx).*ex2; 0050 end 0051 end