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```% GADEMO1 Introduction to the Genetic Optimization Toolbox

% Binary and Real-Valued Simulation Evolution for Matlab
% Copyright (C) 1996 C.R. Houck, J.A. Joines, M.G. Kay
%
% C.R. Houck, J.Joines, and M.Kay. A genetic algorithm for function
% optimization: A Matlab implementation. ACM Transactions on Mathmatical
% Software, Submitted 1996.
%
% This program is free software; you can redistribute it and/or modify
% 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.

clf;
figure(gcf);
more on
echo on
clc
%    ==========================================================
%    ==========================================================

%    INITIALIZE - Initialize a populutaton of solutions
%    GA         - Simulates evolution

pause % Strike any key for the introduction to Genetic Algorithms
clc

%    Genetic algorithms

%    A genetic algorithm is a simulation of evolution where the
%    rule of survival of the fittest is applied to a population
%    of individuals.
%    The basic genetic algorithm is as follows:
%      1. Create an initial population (usually a randomly
%         generated string)
%      2. Evaluate all of the individuals (apply some function
%         or formula to the individuals)
%      3. Select a new population from the old population based
%         on the fitness of the individuals as given by the
%         evaluation function.
%      4. Apply some genetic operators (mutation & crossover)
%         to members of the population to create new solutions.
%      5. Evaluate these newly created individuals.
%      6. Repeat steps 3-6 (one generation) until the
%         termination criteria has been satisfied (usually
%         perform for a certain fixed number of generations)
%
%    Let's look at an example

pause % Strike any key to define the problem...
clc

%   Let's consider the maximization of the following function:
%   f(x) = x + 10*sin(5*x)+7*cos(4*x) over the interval (0,9)
% This may take several minutes...
fplot('x + 10*sin(5*x)+7*cos(4*x)',[0 9])
% Done!

%   Now, let's set up a genetic algorithm to find the maximum
%   of this problem.  First, we need to create the evaluation
%   function .m file, here is gademo1eval1.m

pause 				% Strike any key to look at gademo1eval1.m
pause 					% Strike any key to continue
clc

%   Note that the evaluation function must take two parameters,
%   sol and options.  Sol is a row vector of n+1 elements where
%   the first n elements are the parameters of interest.  The
%   n+1'th element is the value of this solution.  The options
%   matrix is a row matrix of
%   [current generation, eval options]
%   The eval function must return both the value of the sting,
%   val and the string itself, sol.  This is done so that
%   your evaluation can repair and/or improve the string.

pause 					% Strike any key to continue
clc

%   Now that we have defined the evaluation function, we now
%   have to create an initial population.  The most common way
%   to generate an initial population is to randomly generate
%   solutions within the range of interest, in this case 0-9.
%   The initialize routine will do this for you.

pause 				% Strike any key for help on initialize
clc
help initialize
pause 					% Strke any key to continue.
clc
%   Let's create a random starting popluation of size 10.
pause 					% Strike any key to continue.

%   We can now take a look at this population.
hold on
plot (initPop(:,1),initPop(:,2),'g+')
pause % Strike any key to continue
clc
%  We can now run the evolutionary procedure on this
%  population.
help ga
pause 					% Strike any key to continue

% Now let's run the ga for one generation.
[x endPop] = ga([0 9],'gademo1eval1',[],initPop,[1e-6 1 1],'maxGenTerm',1,...
'normGeomSelect',[0.08],['arithXover'],[2],'nonUnifMutation',[2 1 3]);

x %The best found
%And plot the resulting the resulting population
plot (endPop(:,1),endPop(:,2),'ro')
pause 					% Strike any key to continue

% Now let's run the ga for 25 generations
[x endPop] = ga([0 9],'gademo1eval1',[],initPop,[1e-6 1 1],'maxGenTerm',25,...
'normGeomSelect',[0.08],['arithXover'],[2],'nonUnifMutation',[2 1 3]);
x %The best found
% And plot the resulting the resulting population
plot (endPop(:,1),endPop(:,2),'y*')