% GADEMO2 Use of 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% 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.clf;figure(gcf);echo onclc% This demonstration show the use of the genetic toolbox to optimize a% multi-dimensional non-convex function.% The function is coded in the coranaEval.m filepause %Strike any key to examine coranaEvalclctype coranaEval.mpause %Strike any key to continueclc%This function is basically a n dimensional parabola with rectangular%pockets removed. Let's take a look at the function in 2-dimensions%This may take a couple of minutes...i=0;a=-0.5:0.02:0.5;for x=a  i=i+1; j=0;  for y=a    j=j+1;    z(i,j)=coranaEval([x y]);  endend%Done!%First let's look at it in each dimension independentlyclgplot(z(:,1)) %Plot a slice of the function in x max 250.25%Notice the range is [250.0-250.25]pause %Strike any key to continueclgplot(z(1,:)) %Plot a slice of the function in y %Notice the range is [0-250]pause %Strike any key to continuemesh(a,a,z);view(30,60);grid;%Remember the deviation in y is 1000 times that of x.pause %Strike any key to continueclc%Lets minimize this function in 4 dimensions between [-10,000 10,000].%The ga is set up to maximize only.  Minimization of f(x) is equivalent to%maximizing -f(x), so we use the negative of the Corana function.type coranaMin.mpause %Any key to continueclc%First set up the boundsbounds = ones(4,1)*[-10000 10000];%Now lets optimize%This may take some time...[x,endPop,bestSols,trace]=ga(bounds,'coranaMin');%Done!pause %Any key to continueclc%The first return is the optimal [x1 x2 x3 x4 val]x%Lets take a look at the performance of the ga during the runplot(trace(:,1),trace(:,3),'y-')hold onplot(trace(:,1),trace(:,2),'r-')xlabel('Generation'); ylabel('Fittness');%The red line is a track of the best solution, the yellow is a track of the%average of the populationpause %Any key to continueclc%End of gademo2