GA.m

function [Xoptima,FitnessOptimum] = GA(dimensionSize,landscape,landscapeBoundary,populationSize,simulationLimit)
%this version GA (genetic algorithm) is the first version with binary representation so we define that
%mutation is bit flip , and recombination is 1-Point crossover,and the
%resolution is 0.001
%dimensionSize means that each individual have home many demension
global fitnessPoul;
global reproductionProbability;
global mutationRate;
global resolution;
global wholePatchCount;
global theMaxBinaryRepresentation;
global strLength;
global population;
global populationRealVaules;
global intervalVaule;


%pre-definition
fitnessPoul = zeros(populationSize,1);
reproductionProbability = zeros(populationSize,1);
mutationRate = 0.01;
resolution = 0.01;
wholePatchCount = (landscapeBoundary(2)-landscapeBoundary(1)) / resolution;
%count to binary string length
theMaxBinaryRepresentation = dec2bin(wholePatchCount);
strLength = length(theMaxBinaryRepresentation);%the length of each dimension of an individual
individualStrPrensentationLen = dimensionSize*strLength;
%set the mutation rate as the uniform probability to the whole gene
mutationRate = 1/individualStrPrensentationLen;

population = [];
populationRealVaules = [];
intervalVaule = landscapeBoundary(2) - landscapeBoundary(1);

%inital the poputlation
for i = 1 : populationSize,
    tempParent = [];
    tempVaule = [];
    for j = 1:dimensionSize,
        tempNumValue = landscapeBoundary(1)+rand()*intervalVaule;
        tempVaule = [tempVaule,tempNumValue];
        binaryValueStr = transferToString(tempNumValue,landscapeBoundary(1),strLength,resolution);
        tempParent = [tempParent,binaryValueStr];
    end
    %tempParent
    population = [population;tempParent];
    populationRealVaules = [populationRealVaules;tempVaule];
end

%
%fprintf('Initial Data:\n')
%disp(population)
%disp(populationRealVaules);
%
%simulation begin
for i = 1 : simulationLimit,
    %get the reproduction probability
    fitnessPoul = transferFitnessAsPositive(landscape(populationRealVaules));
        %we should transfer the fitnessdata in case of minus value
    denominator = max(fitnessPoul);
    %sumOfFitness = sum(fitnessPoul);
    reproductionProbability = fitnessPoul ./ denominator;
   %reproduction
     %here we should use reproduction probability to determine which part will be
     %the parent
     Offspring = [];
     for j = 1 : populationSize,
        subscript = selectParent(reproductionProbability);
        crossOverPoint = round((individualStrPrensentationLen-1)*rand()+0.01);%0.01 is added in case of rand() = 0
        parentOne = population(subscript(1,1),:);
        parentTwo = population(subscript(1,2),:);
        newSpring = strcat(parentOne(1:(crossOverPoint)),parentTwo((crossOverPoint+1):individualStrPrensentationLen));
        Offspring = [Offspring;newSpring];
     end
   %mutation
   for j = 1 : populationSize,
    dice = rand();
    individualBeChecked = Offspring(j,:);
    if dice <= mutationRate,
        flitLocation = 1 + floor(individualStrPrensentationLen*rand());%mutation is bit-flip,0.01 is added in case of rand() = 0
        individualBeChecked(1,flitLocation) = dec2bin(~individualBeChecked(1,flitLocation));
    end
   end
   %survive
   population = Offspring;
   populationRealVaules = populationStrToRealValue(population,populationSize,dimensionSize,strLength);
end

 fitnessPoul = landscape(populationRealVaules);
 tempSubscript = find(fitnessPoul == max(fitnessPoul));
 bestFitnessSubscript = tempSubscript(1);

FitnessOptimum = fitnessPoul(bestFitnessSubscript);
Xoptima = populationRealVaules(bestFitnessSubscript,:);

    function twoParentsIndex = selectParent(probability)
        count = 0;
        cache = [];
        compareSequence = randperm(populationSize);
        
        while count ~= 2,
        selectProb = rand();    
        for i = 1:populationSize,
            parentIndex = compareSequence(i);
            if selectProb < probability(parentIndex,1),
                if any( cache == parentIndex)==1,%guarantee the two parents are different
                    continue;
                end
                cache = [cache,parentIndex];
                count = count+1;
                break;
            end
        end
        end
        twoParentsIndex = cache;
    end

    function realvaluePresentation = populationStrToRealValue(stringPopulation,populationSize,dimensionSize,strLen)
        realvaluePresentation = [];
        for i = 1:populationSize,
            stringPensentation = stringPopulation(i,:);
            individual = [];
            for j = 1:dimensionSize,
            individual = [individual,transferToNumber(stringPensentation(((j-1)*strLen + 1):j*strLen),landscapeBoundary(1,1),resolution)];
            end
            realvaluePresentation = [realvaluePresentation;individual];
        end
    end
end

function transferedValue = transferFitnessAsPositive(fitnessVector)
%the fitness Vector should be nx1
bottom = min(fitnessVector);
transferedValue = fitnessVector - bottom;
bottom = abs(bottom);
transferedValue = transferedValue + bottom;
end

function geneString = transferToString(number,lowBoundary,stringLength,resolution)
intervalValue = (number - lowBoundary)/resolution;
geneString = dec2bin(intervalValue);
%add extral zeors to the top if the string is not enogh long
divergence = stringLength - length(geneString);
while divergence > 0,
    geneString = strcat('0',geneString);
    divergence = divergence - 1;
end
end

function number = transferToNumber(theString,lowBoundary,resolution)
number = bin2dec(theString);
number = number*resolution + lowBoundary;
end