| devec(NP,D,F,CR,itermax,strategy); |
function [bestmem,nfeval] = devec(NP,D,F,CR,itermax,strategy);
% Run DE minimization
%
% Output arguments:
% ----------------
% bestmem : parameter vector with best solution
% nfeval : number of function evaluations
%
% Input arguments:
% ---------------
% NP : number of population members
% D : number of parameters of the objective
% function
% F : DE-stepsize F ex [0, 2]
% CR : crossover probabililty constant ex [0, 1]
% itermax : maximum number of iterations (generations)
% strategy : 1 --> DE/best/1
% 2 --> DE/rand/1
% 3 --> DE/rand-to-best/1
% 4 --> DE/best/2
% else DE/rand/2
%
% Objective function: has still to be coded into the routine at locations
% designated by >>>>>>>>>>>eval<<<<<<<<<<<<<<<
%
% Example:
% [bestmem,nfeval] = devec(NP,D,F,CR,itermax,strategy);
%
% Used by: dedemov.m
%
% Differential Evolution for MATLAB
% Copyright (C) June 1996 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 two
% properties which differ 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.
% 2) The crossover parameters are chosen randomly, with a probability
% according to a binomial distribution, and need not be adjacent.
% This requires CR usually to be taken larger than in the original
% version of DE.
% Due to the vectorized expressions devec executes fairly fast
% in MATLAB's interpreter environment.
%
% In order to let devec optimize your own objective function you have
% to alter the code as devec was written for simplicity.
%
% 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-----------------------------------------------
if (NP < 5)
fprintf(1,'Error! NP should be >= 5\n');
end
if ((CR < 0) | (CR > 1))
fprintf(1,'Error! CR should be ex [0,1]\n');
end
if (itermax < 0)
fprintf(1,'Error! itermax should be > 0\n');
end
%-----Initialize population and some arrays-------------------------------
pop = zeros(NP,D); %initialize pop to gain speed
lowbound1 = -3; % Lower bound for parameters (all parameters treated alike)
highbound1 = -1; % Upper bound for parameters (all parameters treated alike)
lowbound2 = 1; % Lower bound for parameters (all parameters treated alike)
highbound2 = 3; % Upper bound for parameters (all parameters treated alike)
%----pop is a matrix of size NPxD. It will be initialized-------------
%----with random values between highbound and lowbound----------------
for i=1:NP
pop(i,1) = lowbound1 + rand*(highbound1 - lowbound1);
pop(i,2) = lowbound2 + rand*(highbound2 - lowbound2);
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----------------------
%------Objective function is the Rosenbrock saddle------------------------
%------100*(x2-x1^2)^2+(1-x1)^2.------------------------------------------
ibest = 1; % start with first population member
% >>>>>>>>>>>eval<<<<<<<<<<<<<<<
val(1) = 100*(pop(ibest,2)-pop(ibest,1)^2)^2 + (1-pop(ibest,1))^2;
bestval = val(1); % best objective function value so far
nfeval = nfeval + 1;
for i=2:NP % check the remaining members
% >>>>>>>>>>>eval<<<<<<<<<<<<<<<
val(i) = 100*(pop(i,2)-pop(i,1)^2)^2 + (1-pop(i,1))^2;
nfeval = nfeval + 1;
if (val(i) < bestval) % if member is better
ibest = i; % save its location
bestval = val(i);
end
end
bestmemit = pop(ibest,:); % best member of current iteration
bestvalit = bestval; % best value of current iteration
bestmem = bestmemit; % best member ever
xplt(NP,pop,bestmem,1); % 3D-plot function
%------DE-Minimization---------------------------------------------
%------popold is the population which has to compete. It is--------
%------static through one iteration. pop is the newly--------------
%------emerging population.----------------------------------------
pm1 = zeros(NP,D); % initialize population matrix 1
pm2 = zeros(NP,D); % initialize population matrix 2
pm3 = zeros(NP,D); % initialize population matrix 3
pm4 = zeros(NP,D); % initialize population matrix 4
pm5 = zeros(NP,D); % initialize population matrix 5
bm = zeros(NP,D); % initialize bestmember matrix
ui = zeros(NP,D); % intermediate population of perturbed vectors
mui = zeros(NP,D); % mask for intermediate population
mpo = zeros(NP,D); % mask for old population
rot = (0:1:NP-1); % rotating index array
rt = zeros(NP); % another rotating index array
a1 = zeros(NP); % index array
a2 = zeros(NP); % index array
a3 = zeros(NP); % index array
a4 = zeros(NP); % index array
a5 = zeros(NP); % index array
ind = zeros(4);
iter = 1;
while ((iter < itermax) & (bestval > 1.e-6))
popold = pop; % save the old population
ind = randperm(4); % index pointer array
a1 = randperm(NP); % shuffle locations of vectors
rt = rem(rot+ind(1),NP); % rotate indices by ind(1) positions
a2 = a1(rt+1); % rotate vector locations
rt = rem(rot+ind(2),NP);
a3 = a2(rt+1);
rt = rem(rot+ind(3),NP);
a4 = a3(rt+1);
rt = rem(rot+ind(4),NP);
a5 = a4(rt+1);
pm1 = popold(a1,:); % shuffled population 1
pm2 = popold(a2,:); % shuffled population 2
pm3 = popold(a3,:); % shuffled population 3
pm4 = popold(a4,:); % shuffled population 4
pm5 = popold(a5,:); % shuffled population 5
for i=1:NP % population filled with the best member
bm(i,:) = bestmemit; % of the last iteration
end
mui = rand(NP,D) < CR; % all random numbers < CR are 1, 0 otherwise
mpo = mui < 0.5; % inverse mask to mui
if (strategy == 1) % DE/best/1
ui = bm + F*(pm1 - pm2); % differential variation
ui = popold.*mpo + ui.*mui; % binomial crossover
elseif (strategy == 2) % DE/rand/1
ui = pm3 + F*(pm1 - pm2); % differential variation
ui = popold.*mpo + ui.*mui; % binomial crossover
elseif (strategy == 3) % DE/rand-to-best/1
ui = popold + F*(bm-popold) + F*(pm1 - pm2);
ui = popold.*mpo + ui.*mui; % binomial crossover
elseif (strategy == 4) % DE/best/2
ui = bm + F*(pm1 - pm2 + pm3 - pm4); % differential variation
ui = popold.*mpo + ui.*mui; % binomial crossover
else % DE/rand/2
ui = pm5 + F*(pm1 - pm2 + pm3 - pm4); % differential variation
ui = popold.*mpo + ui.*mui; % binomial crossover
end
%-----Select which vectors are allowed to enter the new population------------
for i=1:NP
% >>>>>>>>>>>eval<<<<<<<<<<<<<<<
tempval = 100*(ui(i,2)-ui(i,1)^2)^2 + (1-ui(i,1))^2; % check cost of competitor
nfeval = nfeval + 1;
if (tempval <= val(i)) % if competitor is better than value in "cost array"
pop(i,:) = ui(i,:); % replace old vector with new one (for new iteration)
val(i) = tempval; % save value in "cost array"
%----we update bestval only in case of success to save time-----------
if (tempval < bestval) % if competitor better than the best one ever
bestval = tempval; % new best value
bestmem = ui(i,:); % new best parameter vector ever
end
end
end %---end for imember=1:NP
bestmemit = bestmem; % freeze the best member of this iteration for the coming
% iteration. This is needed for some of the strategies.
%----Output section----------------------------------------------------------
if (rem(iter,10) == 0)
fprintf(1,'Iteration: %d, Best: %f, F: %f, CR: %f, NP: %d\n',iter,bestval,F,CR,NP);
for n=1:D
fprintf(1,'best(%d) = %f\n',n,bestmem(n));
end
end
%----Continue plotting-------------------------------------------------------
xplt(NP,pop,bestmem,1); % 3D-plot function
iter = iter + 1;
end %---end while ((iter < itermax) ...
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