How to perform Roulette wheel and Rank based selection in a genetic algorithm?

There are different types of selection, we can implement in a genetic algorithm. We sometimes become confused with two types of selection. One is Roulette wheel selection and another is Rank based selection.

In Roulette wheel selection:

• Parents are selected according to their fitness
• The better the chromosomes are, the more chances to be selected they have.

Imagine a roulette wheel where all chromosomes in the population are placed, each chromosome has its place big accordingly to its fitness function, like on the following picture:

This selection will have problems when the finesses differs very much. Outstanding individuals will introduce a bias in the beginning of the search that may cause a premature convergence and a loss of diversity.

For Example:

if an initial population contains one or two very fit but not the best individuals and the rest of the population are not good, then these fit individuals will quickly dominate the whole population and prevent the population from exploring other potentially better individuals. Such a strong domination causes a very high loss of genetic diversity which is definitely not advantageous for the optimization process.

But in Rank Selection:

1. Rank selection first ranks the population and then every chromosome receives fitness from this ranking.
2. The worst will have fitness 1, second worst 2 etc. and the best will have fitness N (number of chromosomes in population).
3. After this all the chromosomes have a chance to be selected.
4. Rank-based selection schemes can avoid premature convergence.
5. But can be computationally expensive because it sorts the populations based on fitness value.
6. But this method can lead to slower convergence, because the best chromosomes do not differ so much from other ones.

So the process will be:

1. First sort the Fitness value of the Population.
2. Then if the Population number is 10 then give the probability of selection to the Population like 0.1,0.2,0.3,…,1.0 .
3. Then calculate cumulative Fitness and make roulette wheel.
4. And the next steps is same as roulette wheel.

My Implementation of Rank Selection in Matlab:

NewFitness=sort(Fitness);
        NewPop=round(rand(PopLength,IndLength));

        for i=1:PopLength
            for j=1:PopLength
                if(NewFitness(i)==Fitness(j))
                    NewPop(i,1:IndLength)=CurrentPop(j,1:IndLength);
                    break;
                end
            end
        end
        CurrentPop=NewPop;

        ProbSelection=zeros(PopLength,1);
        CumProb=zeros(PopLength,1);

        for i=1:PopLength
            ProbSelection(i)=i/PopLength;
            if i==1
                CumProb(i)=ProbSelection(i);
            else
                CumProb(i)=CumProb(i-1)+ProbSelection(i);
            end
        end

        SelectInd=rand(PopLength,1);

        for i=1:PopLength
            flag=0;
            for j=1:PopLength
                if(CumProb(j)<SelectInd(i) && CumProb(j+1)>=SelectInd(i))
                    SelectedPop(i,1:IndLength)=CurrentPop(j+1,1:IndLength);
                    flag=1;
                    break;
                end
            end
            if(flag==0)
                SelectedPop(i,1:IndLength)=CurrentPop(1,1:IndLength);
            end
        end

Note: you can also see my question regarding rank selection here in this link

Thank for reading :). Bye Bye :) :)