%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
     S_bestval      = S_val(k);
  end   
end
FVr_bestmemit = FM_pop(I_best_index,:); % best member of current iteration
S_bestvalit   = S_bestval;              % best value of current iteration

FVr_bestmem = FVr_bestmemit;            % best member ever

%------DE-Minimization---------------------------------------------
%------FM_popold is the population which has to compete. It is--------
%------static through one iteration. FM_pop is the newly--------------
%------emerging population.----------------------------------------

FM_pm1   = zeros(I_NP,I_D);   % initialize population matrix 1
FM_pm2   = zeros(I_NP,I_D);   % initialize population matrix 2