电力系统基于演化算法的无功优化

function [bestmem,bestval,nfeval] = 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 (kprice@solano.community.net) 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 % <jrv@vanzandt.mv.com>, 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: storn@icsi.berkeley.edu % 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--------------------------------------------- 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