devec3.m

模式识别工具箱。非常丰富的底层函数和常见的统计识别工具

function [bestmem,bestval,nfeval, pop] = devec3(fname,VTR,D,XVmin,XVmax,y,NP,itermax,F,CR,strategy,refresh);
% minimization of a user-supplied function with respect to x(1:D),
% using the differential evolution (DE) algorithm of Rainer Storn
% (http://www.icsi.berkeley.edu/~storn/code.html)
%
% Special thanks go to Ken Price ([e-mail]) and
% Arnold Neumaier (http://solon.cma.univie.ac.at/~neum/) for their
% valuable contributions to improve the code.
%
% Strategies with exponential crossover, further input variable
% tests, and arbitrary function name implemented by Jim Van Zandt
% <[e-mail]>, 12/97.
%
% Output arguments:
% ----------------
% bestmem        parameter vector with best solution
% bestval        best objective function value
% nfeval         number of function evaluations
%
% Input arguments:
% ---------------
%
% fname          string naming a function f(x,y) to minimize
% VTR            "Value To Reach". devec3 will stop its minimization
%                if either the maximum number of iterations "itermax"
%                is reached or the best parameter vector "bestmem"
%                has found a value f(bestmem,y) <= VTR.
% D              number of parameters of the objective function
% XVmin          vector of lower bounds XVmin(1) ... XVmin(D)
%                of initial population
%                *** note: these are not bound constraints!! ***
% XVmax          vector of upper bounds XVmax(1) ... XVmax(D)
%                of initial population
% y		        problem data vector (must remain fixed during the
%                minimization)
% NP             number of population members
% itermax        maximum number of iterations (generations)
% F              DE-stepsize F from interval [0, 2]
% CR             crossover probability constant from interval [0, 1]
% strategy       1 --> DE/best/1/exp           6 --> DE/best/1/bin
%                2 --> DE/rand/1/exp           7 --> DE/rand/1/bin
%                3 --> DE/rand-to-best/1/exp   8 --> DE/rand-to-best/1/bin
%                4 --> DE/best/2/exp           9 --> DE/best/2/bin
%                5 --> DE/rand/2/exp           else  DE/rand/2/bin
%                Experiments suggest that /bin likes to have a slightly
%                larger CR than /exp.
% refresh        intermediate output will be produced after "refresh"
%                iterations. No intermediate output will be produced
%                if refresh is < 1
%
%       The first four arguments are essential (though they have
%       default values, too). In particular, the algorithm seems to
%       work well only if [XVmin,XVmax] covers the region where the
%       global minimum is expected. DE is also somewhat sensitive to
%       the choice of the stepsize F. A good initial guess is to
%       choose F from interval [0.5, 1], e.g. 0.8. CR, the crossover
%       probability constant from interval [0, 1] helps to maintain
%       the diversity of the population and is rather uncritical. The
%       number of population members NP is also not very critical. A
%       good initial guess is 10*D. Depending on the difficulty of the
%       problem NP can be lower than 10*D or must be higher than 10*D
%       to achieve convergence.
%       If the parameters are correlated, high values of CR work better.
%       The reverse is true for no correlation.
%
% default values in case of missing input arguments:
% 	VTR = 1.e-6;
% 	D = 2;
% 	XVmin = [-2 -2];
% 	XVmax = [2 2];
%	y=[];
% 	NP = 10*D;
% 	itermax = 200;
% 	F = 0.8;
% 	CR = 0.5;
% 	strategy = 7;
% 	refresh = 10;
%
% Cost function:  	function result = f(x,y);
%                      	has to be defined by the user and is minimized
%			w.r. to  x(1:D).
%
% Example to find the minimum of the Rosenbrock saddle:
% ----------------------------------------------------
% Define f.m as:
%                    function result = f(x,y);
%                    result = 100*(x(2)-x(1)^2)^2+(1-x(1))^2;
%                    end
% Then type:
%
% 	VTR = 1.e-6;
% 	D = 2;
% 	XVmin = [-2 -2];
% 	XVmax = [2 2];
% 	[bestmem,bestval,nfeval] = devec3("f",VTR,D,XVmin,XVmax);
%
% The same example with a more complete argument list is handled in
% run1.m
%
% About devec3.m
% --------------
% Differential Evolution for MATLAB
% Copyright (C) 1996, 1997 R. Storn
% International Computer Science Institute (ICSI)
% 1947 Center Street, Suite 600
% Berkeley, CA 94704
% E-mail: [e-mail]
% WWW:    http://http.icsi.berkeley.edu/~storn
%
% devec is a vectorized variant of DE which, however, has a
% propertiy which differs from the original version of DE:
% 1) The random selection of vectors is performed by shuffling the
%    population array. Hence a certain vector can't be chosen twice
%    in the same term of the perturbation expression.
%
% Due to the vectorized expressions devec3 executes fairly fast
% in MATLAB's interpreter environment.
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 1, or (at your option)
% any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
% GNU General Public License for more details. A copy of the GNU
% General Public License can be obtained from the
% Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

%-----Check input variables---------------------------------------------
global FunCount;
err=[];
if nargin<1, error('devec3 1st argument must be function name'); else
    if exist(fname)<1; err(1,length(err)+1)=1; end; end;
if nargin<2, VTR = 1.e-6; else
    if length(VTR)~=1; err(1,length(err)+1)=2; end; end;
if nargin<3, D = 2; else
    if length(D)~=1; err(1,length(err)+1)=3; end; end;
if nargin<4, XVmin = [-2 -2];else
    if length(XVmin)~=D; err(1,length(err)+1)=4; end; end;
if nargin<5, XVmax = [2 2]; else
    if length(XVmax)~=D; err(1,length(err)+1)=5; end; end;
if nargin<6, y=[]; end;
if nargin<7, NP = 10*D; else
    if length(NP)~=1; err(1,length(err)+1)=7; end; end;
if nargin<8, itermax = 200; else
    if length(itermax)~=1; err(1,length(err)+1)=8; end; end;
if nargin<9, F = 0.8; else
    if length(F)~=1; err(1,length(err)+1)=9; end; end;
if nargin<10, CR = 0.5; else
    if length(CR)~=1; err(1,length(err)+1)=10; end; end;
if nargin<11, strategy = 7; else
    if length(strategy)~=1; err(1,length(err)+1)=11; end; end;
if nargin<12, refresh = 10; else
    if length(refresh)~=1; err(1,length(err)+1)=12; end; end;
if length(err)>0
    fprintf(stdout,'error in parameter %d\n', err);
    usage('devec3 (string,scalar,scalar,vector,vector,any,integer,integer,scalar,scalar,integer,integer)');
end

if (NP < 5)
    NP=5;
    fprintf(1,' NP increased to minimal value 5\n');
end
if ((CR < 0) | (CR > 1))
    CR=0.5;
    fprintf(1,'CR should be from interval [0,1]; set to default value 0.5\n');
end
if (itermax <= 0)
    itermax = 200;
    fprintf(1,'itermax should be > 0; set to default value 200\n');
end
refresh = floor(refresh);

%-----Initialize population and some arrays-------------------------------

pop = zeros(NP,D); %initialize pop to gain speed

%----pop is a matrix of size NPxD. It will be initialized-------------
%----with random values between the min and max values of the---------
%----parameters-------------------------------------------------------

for i=1:NP
    pop(i,:) = XVmin + rand(1,D).*(XVmax - XVmin);
end

popold    = zeros(size(pop));     % toggle population
val       = zeros(1,NP);          % create and reset the "cost array"
bestmem   = zeros(1,D);           % best population member ever
bestmemit = zeros(1,D);           % best population member in iteration
nfeval    = 0;                    % number of function evaluations

%------Evaluate the best member after initialization----------------------

ibest   = 1;                      % start with first population member
val(1)  = feval(fname,pop(ibest,:),y);
bestval = val(1);                 % best objective function value so far
nfeval  = nfeval + 1;
for i=2:NP                        % check the remaining members
    val(i) = feval(fname,pop(i,:),y);
    nfeval  = nfeval + 1;
    if (val(i) < bestval)           % if member is better