GA stepGA - Index exceeds matrix dimensions

Question

I'm writing Custom GA functions in MATLAB for mixed integer problem. More about my problem here and here.

After Roulette Wheel selection is over, Matlab breaks with error:

 Index exceeds matrix dimensions.

Error in stepGA (line 34)
xoverKids  = feval(options.CrossoverFcn, parents(1:(2 * nXoverKids)),options,GenomeLength,FitnessFcn,thisScore,thisPopulation,options.CrossoverFcnArgs{:});

Error in galincon (line 62)
        [score,population,state] = stepGA(score,population,options,state,GenomeLength,FitnessFcn);

Error in ga (line 374)
            [x,fval,exitFlag,output,population,scores] = galincon(FitnessFcn,nvars, ...

It breaks in stepGA.m at:

xoverKids  = feval(options.CrossoverFcn, parents(1:(2 * nXoverKids)),options,GenomeLength,FitnessFcn,thisScore,thisPopulation,options.CrossoverFcnArgs{:});

More precisely at parents(1:(2 * nXoverKids)).

My variables at that time:

nXoverKids = 7
nParents = 16
nEliteKids = 1
nMutateKids = 2
parents = 1 1

My Roullete wheel selection:

function parents = RouletteWheelSelection(expectation, nParents, options)
% ---------------------------------------------------------
% Roulette Wheel Selection Algorithm. A set of weights
% represents the probability of selection of each
% individual in a group of choices. It returns the chosen chromosome.
% ---------------------------------------------------------
  r1 = rand;
  r2 = rand;
  index1 = sum(r1 >= cumsum([0, expectation']));
  index2 = sum(r2 >= cumsum([0, expectation']));

  parents = [index1, index2];
end

From Matlab documentation:

The function returns parents, a row vector of length nParents containing the indices of the parents that you select.

Am I returning wrong from Selection? And why are nParents set at 16?

My other options for GA:

options = gaoptimset(...
                      'PopulationSize',    10, ...
                      'Generations',       50, ...
                      'InitialPopulation', population.chromosomes(1,:),...
                      'SelectionFcn',      @RouletteWheelSelection, ...
                      'CrossoverFcn',      @Crossover, ...
                      'MutationFcn',       @Mutation
                     );
lb = 1;  % Lower bound on x
ub = 3;  % Upper bound on x
nvars = 81;

rules = population.chromosomes(1, :);



 x = ga(@(x)GaFitness(rules, sim_obj, EV_input_time_first, EV_input_time_second, inpxpath, layxpath, Results),...
       nvars,[],[],[],[],lb,ub,[],[],options);    

Also my InitialPopulation population.chromosomes(1,:) is 1x81 size.

Answer 1

• RouletteWheelSelection doesn't return parents with 2 individuals

• Assuming the population contains 10 individuals
• During RouletteWheelSelection you'll be asked to choose nParents out of the 10, 5 for example

Obviously nParents should not exceed PopulationSize

You have set nParents = 16 while PopulationSize = 10

• The correct word will be nIndividuals instead of nParents
• expectation means probability, a value comprised between 0 and 1, also called relative fitness

expectation(individual_1) = fitness(individual_1)/sum(fitness(ALL_individuals)); 

Illustrative example on ga parameters setting

% lower bound
lb = -2;
% upper bound
ub = 2;

% Population size
individuals = 10;
% Fitness function
fitness = @(x) -x.^2;

% Given population, 10 individuals

pop = linspace(lb, ub, individuals);

% All Population individuals Fitness
pop_fitness = fitness(pop);

% All Population individuals relative Fitness 
rfit = pop_fitness./sum(pop_fitness);

% All Population individuals cumulative fitness, sum up to 1
cumulative_relative_fit = cumsum(rfit);

% Number of individuals to be selected out of 10
nparents = 5;
sel = zeros(1, nparents);

% Indices of individuals in population
index = 1:numel(pop);

% Roulette Wheel Selection starts here

for i = 1 : nparents
    rnd = rand;
if rnd <=  cumulative_relative_fit(1)
    % Selected the first individual 
    % if first Cumulative relative fitness is higher than
    % generated random number 
    sel(i) = 1;
else
     % Find indices where generated random number is higher than 
     % Cumulative relative fitness
     ind = rnd >=  cumulative_relative_fit;
     
     
     ALL_Indices_Above_Cum = index(ind);
     % Choose the one with the highest Cumulative relative fitness
     sel(i) = ALL_Indices_Above_Cum(end);
end

end

Selected Individuals

nParents = 5;
Population Size = 10;
sel = [4     9     1     7     1];

---

Change your custom selection function to this

function parents = RouletteWheelSelection(expectation, nParents, 'ga')
% ---------------------------------------------------------
% Roulette Wheel Selection Algorithm. A set of weights
% represents the probability of selection of each
% individual in a group of choices. It returns the chosen chromosome.
% ---------------------------------------------------------
    % Population individuals indices
    index = 1 : numel(expectation);
    
    % Indices of individuals to be selected 
    parents = zeros(1, nParents);

    % Cumulative relative fitness, the last one is 1
    cumulative_relative_fit = cumsum(expectation); 
    
    
    for i = 1:  nParents
        rnd = rand;
        % Selected the first individual 
        % if first Cumulative relative fitness is higher than
        % generated random number 
        
        if rnd <=  cumulative_relative_fit(1)
            parents(i) = 1;
        else
             % Find indices where generated random number is higher than 
             % Cumulative relative fitness
             ind = rnd >=  cumulative_relative_fit;

             ALL_Indices_Above_Cum = index(ind);
             % Choose the one with the highest Cumulative relative fitness            
             parents(i) = ALL_Indices_Above_Cum(end);
        end
    end
 
end