Erroneous error: Index exceeds the number of array elements. Index must not exceed 0. Any idea on how to fix this problem?

Hey guys I am having a problem with a Matlab code of mine. The code is a genetic alogrithm that should find the parameters a1, a2, a3, b1, b2, b3 for this following function:

The code is composed of a main function called GAFunctionFinder.m and 6 functions that the main script calls, as following:

GAFunctionFinder.m

populationSize = 100;           % modify as desired (but should be even)
numberOfGenerations = 10000;    % modify as desired
maximumParameterValue = 2;      % parameters range from -2 to 2 (do not change)
tournamentProbability = 0.75;   % modify as desired
crossoverProbability = 0.75;    % modify as desired
mutationProbability = 0.125;    % modify as desired
creepProbability = 0.5;         % modify as desired
creepRate = 0.01;               % modify as desired

functionData = LoadFunctionData();

format long

numberOfParameters = 6;
bestIndividual = zeros(numberOfParameters, 1); %% Best values of the a_i and b_i parameters

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initialize population
%%%%%%%%%%%%%%%%%%%%%%%%%%%%

population = InitializePopulation(populationSize, numberOfParameters); 

fitness = zeros(populationSize,1);
maximumFitness = 0.0;
for iGeneration = 1:numberOfGenerations

  maximumFitnessInCurrentGeneration = 0;  

  %%%%%%%%%%%%%%%%%%%%%%%%%%%
  % Evaluate individuals
  %%%%%%%%%%%%%%%%%%%%%%%%%%%
  for i = 1:populationSize
    chromosome = population(i,:);
    fitness(i) = EvaluateIndividual(chromosome,functionData);  %% Write this function
    if (fitness(i) > maximumFitnessInCurrentGeneration)  
      maximumFitnessInCurrentGeneration = fitness(i);
      iBestIndividual = i;
      if (fitness(i) > maximumFitness)
       maximumFitness = fitness(i);
       bestIndividual = chromosome;
       fprintf('%d %12.8f\n',iGeneration, maximumFitness);
      end
    end
  end

  %% Add plot of maximum fitness, either here or at the end of the
  %% run. In the latter case, at least make sure to store the 
  %% maximum fitness for each generation, so that you can later make the plot.

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  % Generate new population, unless the last generation has been evaluated
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   if (iGeneration < numberOfGenerations)
     temporaryPopulation = population;  
     for i = 1:2:populationSize
       i1 = TournamentSelect(fitness,tournamentProbability);    %% Write this function
       i2 = TournamentSelect(fitness,tournamentProbability);    %% Write this function
       r = rand;
       if (r < crossoverProbability) 
         chromosome1 = population(i1,:);
         chromosome2 = population(i2,:);
         newIndividualPair = Cross(chromosome1, chromosome2);   %% Write this function
         temporaryPopulation(i,:) = newIndividualPair(1,:);
         temporaryPopulation(i+1,:) = newIndividualPair(2,:);
       else
         temporaryPopulation(i,:) = population(i1,:);
         temporaryPopulation(i+1,:) = population(i2,:);
       end
     end
     temporaryPopulation(1,:) = population(iBestIndividual,:);  %% Elitism, prevents maximum fitness from decreasing.
     for i = 2:populationSize
       originalChromosome = temporaryPopulation(i,:);
       mutatedChromosome = Mutate(originalChromosome, mutationProbability,creepProbability,creepRate);  %% Write this function
       temporaryPopulation(i,:) = mutatedChromosome;
     end
     population = temporaryPopulation;
   end
end

LoadFunctionData.m:

function functionData = LoadFunctionData

functionData = load('data_ga.txt')

InitializePopulation.m:

function population = InitializePopulation(populationSize, numberOfParameters)
    population = -2 + (4*rand(populationSize, numberOfParameters));
end

EvaluateIndividual.m:

function fitness = EvaluateIndividual(chromosome, functionData)
% This function generates (as output) the fitness value; see the problem
% formulation for details. Note: It is not always a good idea to pass a data
% set as a parameter, but here the data set is small, so it is OK.
    g = @(x,y) (1+chromosome(1)*x+chromosome(2)*x.^2+chromosome(3)*x.^3) ./ ...
               (1+chromosome(4)*y+chromosome(5)*y.^2+chromosome(6)*y.^3);
    f = @(g,g_hat) sqrt(mean((g - g_hat).^2));
    x = functionData(:,1);
    y = functionData(:,2);
    g_hat = g(x,y);
    g_true = functionData(:,3);
    fitness = exp(-f(g_true, g_hat));
end

TournamentSelect.m

function selectedIndex = TournamentSelect(fitness, tournamentProbability)
    populationSize = length(fitness);
    tournamentSize = 2;
    tournamentWinners = zeros(1, tournamentSize);
    for i = 1:tournamentSize
        candidates = randperm(populationSize, tournamentSize);
        candidateFitnesses = fitness(candidates);
        [~, winnerIndex] = max(candidateFitnesses);
        tournamentWinners(i) = candidates(winnerIndex);
    end
    selectedIndex = tournamentWinners(rand < tournamentProbability) ;
end

Cross.m

function newIndividualPair = Cross(chromosome1, chromosome2)
    n = length(chromosome1);
    crossoverPoint = randi([2, n-1]); % Ensure that crossover point is not too close to the ends
    offspring1 = [chromosome1(1:crossoverPoint) chromosome2(crossoverPoint+1:end)];
    offspring2 = [chromosome2(1:crossoverPoint) chromosome1(crossoverPoint+1:end)];
    newIndividualPair=[offspring1;offspring2];
end

Mutate.m

function mutatedChromosome = Mutate(originalChromosome, mutationProbability, creepProbability, creepRate)
% originalChromosome: the chromosome to be mutated
% mutationProbability: the probability of each gene being mutated
% creepProbability: the probability of a gene undergoing a creep mutation
% creepRate: the magnitude of the creep mutation

% Get the chromosome length
chromLen = length(originalChromosome);

% Initialize the mutated chromosome
mutatedChromosome = originalChromosome;

% Loop through all genes in the chromosome
for i = 1:chromLen
    % Check if the gene should be mutated
    if rand < mutationProbability
        % Decide whether to do a creep mutation or full-range mutation
        if rand < creepProbability
            % Creep mutation
            mutatedChromosome(i) = mutatedChromosome(i) + creepRate * (rand - 0.5);
        else
            % Full-range mutation
            mutatedChromosome(i) = rand;
        end
    end
end

So without getting into too much details, the error I am getting has to do with the cross function. When I run the code from the main script I basically get two types of error:

Unable to perform assignment because the size of the left side is 1-by-6 and the size of the right side is 0-by-6.

Error in GAFunctionFinder (line 104)
         temporaryPopulation(i+1,:) = population(i2,:);
%%%%OR
Index exceeds the number of array elements. Index must not exceed 0.

Error in Cross (line 38)
    offspring2 = [chromosome2(1:crossoverPoint) chromosome1(crossoverPoint+1:end)];

Error in GAFunctionFinder (line 99)
         newIndividualPair = Cross(chromosome1, chromosome2);   %% Write this function

This is a bit confusing as without changing anything in the code I am getting two different errors depending on the run. The error is not in the main files as I've been handed this script. The error should be in the cross function. Although I have used different approaches to solve this problem, I am still getting the same errors over and over again. So in this cross function below, I have tried changing IMIN in the randi from 2 to 1, without any luck. Also, what this functions does, in short terms, is that it randomly select a crossover point, and this crossover point is then used to generate a new pair of chromosomes called offsprings.

         function newIndividualPair = Cross(chromosome1, chromosome2)
    n = length(chromosome1);
    crossoverPoint = randi([2, n-1]); % Ensure that crossover point is not too close to the ends
    offspring1 = [chromosome1(1:crossoverPoint) chromosome2(crossoverPoint+1:end)];
    offspring2 = [chromosome2(1:crossoverPoint) chromosome1(crossoverPoint+1:end)];
    newIndividualPair=[offspring1;offspring2];
end

If anyone has an idea, it would be greatly appreciated!

Answer 1

[Torsten]

rand < tournamentProbability becomes "false" for all elements of "tournamentProbability" in "TournamentSelect". Thus the output of the function is empty.

[Christian Tsobanoglou]

Much appreciated, thank you!