gaGnuOct.m

function [x popx fitvals] = gaGnuOct(ffit, nbits, gaOptions, varargin)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  Description: Essence of a Genetic Algorithm for Matlab or Gnu Octave.  %%
%%  Author: Laboratory of Bioinformatics UFPR/SEPT - Roberto Tadeu Raittz. %%
%%  Adaptation: Eduardo Lemons Francisco - Hexabio Bioinformatics.         %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Function:  Runs a canonic (binary) genetic algorithm.
%
% Example:
%            x = gaGnuOct(@fitnessFunction, numberOfBits, gaOptions);
%
%  "x" receives numberOfBits bits optimized according to the user function 'fitnessFunction';
%  gaOptions is an struct compatible with that generated by Matlab "gaoptimset" or
%  one struct var that contains at least the parameters:
%
%       gaOptions.InitialPopulation
%       gaOptions.PopulationSize
%       gaOptions.Generations
%       gaOptions.EliteCount
%       gaOptions.MutationRate
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Initialization %%

m = nbits;
n = gaOptions.PopulationSize;
nger = gaOptions.Generations;
mutrate = gaOptions.MutationRate;	%% Uses only uniform mutation rate (number 0..1)
nelite = gaOptions.EliteCount;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if isempty(gaOptions.InitialPopulation)
    pop0 = logical(randi(2,n,m)-1);
else
    pop0 = gaOptions.InitialPopulation;
end
if isempty(mutrate) || iscell(mutrate)
    mutrate = 0.15;
end    
if isempty(nelite)
    nelite = 2;
end    
nmut = fix(mutrate*n);
popx = pop0;
fits = zeros(n,1);

%% Generations %%
for j=1:nger
    for i=1:n
        fits(i) = ffit(popx(i,:));
    end
    [xx iord] = sort(fits);
    %disp(['Generation: ' num2str(j) "\t\tElite: " num2str(xx(1:nelite)')]);
    popx = popx(iord,:);
    newpop = popx;
    %% Crossing-over %%
    i1 = randipow(n,1.3,n,1);
    i2 = randipow(n,1.3,n,1);
    pop1 = popx(i1,:);
    pop2 = popx(i2,:);
    icros = repmat(randi(m,n,1),1,m);
    ids = repmat(1:m,n,1);
    crt = (ids>icros);
    newpop(crt) = pop1(crt);
    newpop(~crt) = pop2(~crt);
    %% Mutation %%
    if nmut>0
        popmut = newpop(1:nmut,:);
        ids = find(popmut | ~popmut);
        xmut = randi(length(ids),nmut,1);
        popmut(xmut) = ~popmut(xmut);
    end
    %% Elitism %%
    if nelite>0
        newpop(1:nelite,:) = popx(1:nelite,:);
    end
    %% Create new population %%
    newpop(1+nelite:nelite+nmut,:) = popmut;
    popx = newpop;
end
%% Returns %%
[fitvals iord] = sort(fits);
popx = popx(iord,:);
x = popx(1,:);

%% Used for selection, see: http://www.sbgames.org/papers/sbgames08/posters/papers/p19.pdf %%
function M = randipow(xmax,xpow,n, m)
	M = fix((xmax)*(rand(n,m).^xpow)) + 1;