%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
