%
% Written by:
% -- 
% John L. Weatherwax                2006-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear; close all; %clc; 

addpath('../Chapter1');

% Parameters used in the genetic algorithm
% 
N_gene = 50; % the discreteness of the floating point representations
X_rate = 0.5; % selection rate 
max_number_of_iterations = 5; 

% method to select mates:
%   1=> pairing from top to bottom
%   2=> random pairing
%   3=> random pairing (rank weighting)
%   4=> weighted random pairing (cost weighting)
%   5=> tournament selection 
%
parent_selection_method = 3; 

% method used to do crossover:
%   1=> single point crossover
%   2=> double point crossover 
%   3=> uniform crossover 
%
crossover_method = 1;

% a function to minimize (and its bounds)
%
funnum = 8;
bounds = [ -10, +10 ; -10, +10 ]; % the functions domain 

wfn = @(x) testfunction(x,funnum); % our function handle can evaluate an entire population 


%
% STUDY THE CHANGE IN THE EFFECT OF MU:
%
N_pop = 50; % a very small the population size but fixed 

nMCSamples = 100; % the number of monte carlo samples 

% Consider various values of mu
muArray = linspace( 0.01, 0.5, 20 );
avg_min_fn = zeros(1,length(muArray));
std_min_fn = zeros(1,length(muArray));
for mui = 1:length(muArray) 
  fprintf('working on %6d monte carlo runs for mu= %6.4f\n',nMCSamples,muArray(mui));
  f_min_sample = zeros(1,nMCSamples);
  for ii=1:nMCSamples, % a random draw
    
    [pop,pop_costs,best_fn_values,avg_fn_values] = binary_GA( wfn, bounds, N_pop, N_gene, X_rate, muArray(mui), max_number_of_iterations, parent_selection_method, crossover_method );
    f_min_sample(ii) = best_fn_values( max_number_of_iterations );
    
  end
  
  % compute statistics over this minium: 
  avg_min_fn(mui) = mean( f_min_sample );
  std_min_fn(mui) = std( f_min_sample ); 
  
end

figure; 
av = plot( muArray, avg_min_fn, '-rx' ); hold on; 
avm = plot( muArray, avg_min_fn-std_min_fn, '-g' ); 
avp = plot( muArray, avg_min_fn+std_min_fn, '-g' ); 
legend( [av,avp,avm], {'average','lower 1 sigma CI','upper 1 sigma CI'}, 'location', 'best' );
xlabel('value of mu'); ylabel('average of the smallest function value');

%saveas(gcf,'../../WriteUp/Graphics/Chapter2/variations_in_mu_MC.eps','epsc');


%
% STUDY THE CHANGE IN THE EFFECT OF N_pop:
%
mu = 0.02; % the fixed mutation rate 

N_pop = 50; % a very small the population size

nMCSamples = 100; % the number of monte carlo samples 

% Consider various values of N_pop
NArray = 50:50:1000;
avg_min_fn = zeros(1,length(NArray));
std_min_fn = zeros(1,length(NArray));
for ni = 1:length(NArray) 
  fprintf('working on %6d monte carlo runs for N_pop= %6d\n',nMCSamples,NArray(ni));
  f_min_sample = zeros(1,nMCSamples);
  for ii=1:nMCSamples, % a random draw
    
    [pop,pop_costs,best_fn_values,avg_fn_values] = binary_GA( wfn, bounds, NArray(ni), N_gene, X_rate, mu, max_number_of_iterations, parent_selection_method, crossover_method );
    f_min_sample(ii) = best_fn_values( max_number_of_iterations );
    
  end
  
  % compute statistics over this minium: 
  avg_min_fn(ni) = mean( f_min_sample );
  std_min_fn(ni) = std( f_min_sample ); 
  
end

figure; 
av = plot( NArray, avg_min_fn, '-rx' ); hold on; 
avm = plot( NArray, avg_min_fn-std_min_fn, '-g' ); 
avp = plot( NArray, avg_min_fn+std_min_fn, '-g' ); 
legend( [av,avp,avm], {'average','lower 1 sigma CI','upper 1 sigma CI'}, 'location', 'best' );
xlabel('value of N_{pop}'); ylabel('average of the smallest function value');

%saveas(gcf,'../../WriteUp/Graphics/Chapter2/variations_in_N_pop.eps','epsc');