% Rastrigin function L. LAURENT -- 21/02/2012 -- luc.laurent@lecnam.net
0001 %% Rastrigin function 0002 %L. LAURENT -- 21/02/2012 -- 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 minimum global: x=(0,0,...,0) >> f(x)=0 0027 % 0028 %Design space -5.12<xi<5.12 0029 % 0030 %[TZ89] A. T\šorn and A. Zilinskas. "Global Optimization". Lecture Notes in Computer Science, No 350, Springer-Verlag, Berlin,1989. 0031 %[MSB91] H. M\šuhlenbein, D. Schomisch and J. Born. "The Parallel Genetic Algorithm as Function Optimizer ". Parallel Computing, 17, pages 619-632,1991. 0032 0033 0034 function [p,dp]=funRastrigin(xx) 0035 0036 %constants 0037 coef=10; 0038 nbvar=size(xx,3); 0039 0040 %evaluation and derivatives 0041 cal=xx.^2-coef*cos(2*pi*xx); 0042 p=coef*nbvar+sum(cal,3); 0043 0044 if nargout==2 0045 dp=2*xx+2*coef*pi*sin(2*pi*xx); 0046 end 0047 end