微分进化算法DEMATLAB源程序-DeMat.rar

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Function: [FVr_bestmem,S_bestval,I_nfeval] = deopt(fname,S_struct) % % Author: Rainer Storn, Ken Price, Arnold Neumaier, Jim Van Zandt % Description: Minimization of a user-supplied function with respect to x(1:I_D), % using the differential evolution (DE) algorithm. % DE works best if [FVr_minbound,FVr_maxbound] covers the region where the % global minimum is expected. DE is also somewhat sensitive to % the choice of the stepsize F_weight. A good initial guess is to % choose F_weight from interval [0.5, 1], e.g. 0.8. F_CR, the crossover % probability constant from interval [0, 1] helps to maintain % the diversity of the population but should be close to 1 for most. % practical cases. Only separable problems do better with CR close to 0. % If the parameters are correlated, high values of F_CR work better. % The reverse is true for no correlation. % % The number of population members I_NP is also not very critical. A % good initial guess is 10*I_D. Depending on the difficulty of the % problem I_NP can be lower than 10*I_D or must be higher than 10*I_D % to achieve convergence. % % deopt is a vectorized variant of DE which, however, has a % property which differs from the original version of DE: % 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 deopt executes fairly fast % in MATLAB's interpreter environment. % % Parameters: fname (I) String naming a function f(x,y) to minimize. % S_struct (I) Problem data vector (must remain fixed during the % minimization). For details see Rundeopt.m. % ---------members of S_struct---------------------------------------------------- % F_VTR (I) "Value To Reach". deopt will stop its minimization % if either the maximum number of iterations "I_itermax" % is reached or the best parameter vector "FVr_bestmem" % has found a value f(FVr_bestmem,y) <= F_VTR. % FVr_minbound (I) Vector of lower bounds FVr_minbound(1) ... FVr_minbound(I_D) % of initial population. % *** note: these are not bound constraints!! *** % FVr_maxbound (I) Vector of upper bounds FVr_maxbound(1) ... FVr_maxbound(I_D) % of initial population. % I_D (I) Number of parameters of the objective function. % I_NP (I) Number of population members. % I_itermax (I) Maximum number of iterations (generations). % F_weight (I) DE-stepsize F_weight from interval [0, 2]. % F_CR (I) Crossover probability constant from interval [0, 1]. % I_strategy (I) 1 --> DE/rand/1 % 2 --> DE/local-to-best/1 % 3 --> DE/best/1 with jitter % 4 --> DE/rand/1 with per-vector-dither % 5 --> DE/rand/1 with per-generation-dither % 6 --> DE/rand/1 either-or-algorithm % I_refresh (I) Intermediate output will be produced after "I_refresh" % iterations. No intermediate output will be produced % if I_refresh is < 1. % % Return value: FVr_bestmem (O) Best parameter vector. % S_bestval.I_nc (O) Number of constraints % S_bestval.FVr_ca (O) Constraint values. 0 means the constraints % are met. Values > 0 measure the distance % to a particular constraint. % S_bestval.I_no (O) Number of objectives. % S_bestval.FVr_oa (O) Objective function values. % I_nfeval (O) Number of function evaluations. % % Note: % 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. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [FVr_bestmem,S_bestval,I_nfeval] = deopt(fname,S_struct) %-----This is just for notational convenience and to keep the code uncluttered.-------- I_NP = S_struct.I_NP; F_weight = S_struct.F_weight; F_CR = S_struct.F_CR; I_D = S_struct.I_D; FVr_minbound = S_struct.FVr_minbound; FVr_maxbound = S_struct.FVr_maxbound; I_bnd_constr = S_struct.I_bnd_constr; I_itermax = S_struct.I_itermax; F_VTR = S_struct.F_VTR; I_strategy = S_struct.I_strategy; I_refresh = S_struct.I_refresh; I_plotting = S_struct.I_plotting; %-----Check input variables--------------------------------------------- if (I_NP < 5) I_NP=5; fprintf(1,' I_NP increased to minimal value 5\n'); end if ((F_CR < 0) | (F_CR > 1)) F_CR=0.5; fprintf(1,'F_CR should be from interval [0,1]; set to default value 0.5\n'); end if (I_itermax <= 0) I_itermax = 200; fprintf(1,'I_itermax should be > 0; set to default value 200\n'); end I_refresh = floor(I_refresh); %-----Initialize population and some arrays------------------------------- FM_pop = zeros(I_NP,I_D); %initialize FM_pop to gain speed %----FM_pop is a matrix of size I_NPx(I_D+1). It will be initialized------ %----with random values between the min and max values of the------------- %----parameters----------------------------------------------------------- for k=1:I_NP FM_pop(k,:) = FVr_minbound + rand(1,I_D).*(FVr_maxbound - FVr_minbound); end FM_popold = zeros(size(FM_pop)); % toggle population FVr_bestmem = zeros(1,I_D);% best population member ever FVr_bestmemit = zeros(1,I_D);% best population member in iteration I_nfeval = 0; % number of function evaluations %------Evaluate the best member after initialization---------------------- I_best_index = 1; % start with first population member S_val(1) = feval(fname,FM_pop(I_best_index,:),S_struct); S_bestval = S_val(1); % best objective function value so far I_nfeval = I_nfeval + 1; for k=2:I_NP % check the remaining members S_val(k) = feval(fname,FM_pop(k,:),S_struct); I_nfeval = I_nfeval + 1; if (left_win(S_val(k),S_bestval) == 1) I_best_index = k; % save its location