%%% How to use the GA algorithm

%%% Minimisation of Rosenbrock's function, a common 
%%% test function for optimizers. 
%%% The function is a sum of squares

%%% The function has a minimum value of zero at the point 
%%% [1,1]. Because the Rosenbrock's function is quite steep, plot 
%%% the logarithm of one plus the function.

%fsurf(@(x,y) log(1 + 100*(x.^2 - y).^2 + (1 - x).^2),[0,2])
fsurf(@(x,y) 100*(x.^2 - y).^2 + (1 - x).^2,[0,2])
title('1 + 100*(x(1)^2 - x(2))^2 + (1 - x(1))^2')
view(-13,78)
hold on
h1 = plot3(1,1,0.1,'r*','MarkerSize',12);
legend(h1,'Minimum','Location','best');
hold off

%%%
%%% Minimize Using ga
%%%
%%% To minimize the fitness function using GA, pass 
%%% a function handle to the fitness function, as 
%%% well as the number of variables in the problem. 
%%% To have GA examine the relevant region, include 
%%% bounds -3 <= x(i) <= 3. 
%%% Pass the bounds as the fifth and sixth arguments 
%%% after numberOfVariables. For ga syntax details, 
%%% see ga.
%%%
%%% ga is a random algorithm. For reproducibility, 
%%% set the random number stream.

rng default % For reproducibility
FitnessFunction = @simple_fitness;
numberOfVariables = 2;

options = optimoptions('ga','InitialPopulationRange',[1;100],...
    'PlotFcn',{@gaplotbestf,@gaplotdistance});

% Include plot functions to monitor the optimization process.
options = optimoptions(@ga,'PlotFcn',{@gaplotbestf,@gaplotstopping});

fminuncOptions = optimoptions(@fminunc,'PlotFcn',...
    {'optimplotfval','optimplotx'});
options = optimoptions(options,'HybridFcn',...
    {@fminunc, fminuncOptions});

[x,fval] = ga(FitnessFunction,numberOfVariables,[],[],[],[],[],[],...
              [],options)

         
return          

%%%
%%% Function to be minimised
%%%


function y = simple_fitness(x)
%SIMPLE_FITNESS fitness function for GA
 
  y = 100 * (x(1)^2 - x(2)) ^2 + (1 - x(1))^2;
  
end