Evolve

Using The GATOOL in MATLAB

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The gatool in MATLAB provides researchers with the ability to quickly apply optimization techniques to problems that need a genetic algorithm. As with all toolboxes contained in MATLAB the gatool has a command line interface and a GUI interface. We will be using the GUI interface since it provides an easier means of modifying the parameters of the toolbox. The gatool implements a canonical genetic algorithm, with the ability to provide custom functions for mutation, crossover and selection operators. Before going any further lets review Introduction To MathWorks MATLAB. Now that you are back lets see how this can be done.

We will need to create two functions for use with the gatool (1)objective function, (2)creation function. The objective function will be minimized by the genetic algorithm to give an ideal solution for our problem definition. While the creation function will be used to create initial individuals for the genetic algorithm population.

Objective Function:

function rtn = objective(param)
seq = [1 2 3 4 5];
temp = 5;
for i = 1:length(param)
 if eq(seq(i),floor(param(i)))
 temp = temp - 1;
 end
end
rtn = temp;

Creation Function:

function rtn = creator(genomeLength, fitnessFn, options)
temp = floor(5.*rand(5,1));
rtn = temp';

Gocha’s: Arguements for the respective functions must be provided otherwise the toolbox will not be able to provide the necessary parameters to the functions.

Launch gatool-> Type gatool in the MATLAB command window

GATOOL Interface: Only parameters marked in red were modified.

Results: Click the start button on the gatool to start the optimization routine.

Results Plot:

Conclusion:
This post intends to use the gatool present in MATLAB to evolve a vector of integers from 1 to 5. If you take the floor of the final point listings you will see that this aim was achieved with 0.0 fitness.  As an exercise you could modify the other parameters present in the gatool and re-run the routine to observe any changes that may occur.

Simple Genetic Algorithm To Evolve A String of Integers

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Genetic Algorithms are a means of optimization copied from the natural world. According to the theories of evolution, nature has a way of selecting the best (fittest) individuals to mate (Crossover) and reproduce; thus carrying on the best features of each selected individual. Even though traits from both parents are carried over into children there is still an element of randomness involved (Mutation) that gives their offspring the ability to explore their fitness landscape (adapt) to their environment. Genetic Algorithms tries to mimic this behavior with three common operators (1)Selection, (2)Crossover, (3)Mutation.

Selection:  
The selection operator determines how the individuals of a population are selected to mate, the most popular selection method is called elitism and this is the method that we will use in our genetic algorithm implementation.

Crossover:
The crossover operator determines how the parents are recombined to form offspring. We will be using single point crossover in this implementation.

Mutation:
Mutation inserts randomness into the genotype of each offspring giving it the ability to diversify from the features of its parents.

Note
Implementing genetic algorithms can be seen as somewhat of an art because almost all of the code is boiler plate except for the chromosome representation used and how the fitness of each individual is calculated. These two factors usually have the most impact on the accuracy and speed of the genetic algorithm and are the most difficult to represent. These factors along with the mutation rate, crossover rate and selection method have to be tinkered with until a viable configuration is reached.

This implementation will evolve the number sequence 123456789 in that specific order.

Interesting Functions

private static void CalculateFitness(sequence seq)
{
var ordered = new sequence{buffer = new List<string>() {"1", "2", "3", "4", "5", "6", "7", "8", "9"}};

int result=0;
for (int i = 0; i < 9; i++)
{
if (ordered.buffer[i] == seq.buffer[i]) result++;
}
seq.fitness = result;
}

 

private void Epoch(List<sequence> population)
        {
            //Elitism
            survivors.AddRange(population.Where(i => i.fitness >= survivorThreshold));

            Mutate(population.Where(i => i.fitness >= mutantThreshold));

            CrossOver(population.Where(i => i.fitness >= crossoverThreshold) as IEnumerable);

            population.Clear();
            population.AddRange(survivors);

            for (int i = 0; i < populationSize - survivors.Count; i++)
            {
                var temp = GenerateSequence();
                CalculateFitness(temp);
                population.Add(temp);
            }
            survivors.Clear();
        }

The full code listing can be found at github