funRastrigin

PURPOSE ^

% Rastrigin function

SYNOPSIS ^

function [p,dp]=funRastrigin(xx)

DESCRIPTION ^

% Rastrigin function
L. LAURENT -- 21/02/2012 -- luc.laurent@lecnam.net

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

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

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