binary-coded-genetic-algorithm

Five phases are considered in a genetic algorithm: I. Initial population II. Fitness function III. Selection IV. Crossover V. Mutation

Two cases were studied in this project:

---

A. Binary Coded data

I. Initial Population: The population is created randomly, consisting of zeros and ones, as follows: pop =round(rand(Npop,N));

II. Fitness function
We intent to optimize the number of one bits of the chromosome in the population. The activation function is the number of zeros in the chromosomes:

	function z=MinOnek(nb_bit,x)
    	z=nb_bit - sum(x);
	end

III. Selection
By classifying individuals from 1 to Npop according to their value according to function J. By each time pulling the individual with the probability:

1. Wheel:

  function [r] = selection(sumc,Npop)
   n=rand();
 	  r=1;
	   while (sumc(r) < n && r<=Npop)
  	      r=r+1;
 	    end
  end

2. Random:

  function [r] = selectionrandom(Npop)
     r=randi([1 Npop]);
  end

IV. Crossover It consists in randomly drawing an integer between 1 and N-1 and in exchanging, with a probability Pc.

1. Single Point Crossover

for i=1:2:Npop
        if(pc > rand())
            index=round((N-2)*rand())+1;
            newpop(i,1:index)=pop(i,1:index);
            newpop(i,index+1:N)=pop(i+1,index+1:N);
 
            newpop(i+1,1:index)=pop(i+1,1:index);
            newpop(i+1,index+1:N)=pop(i,index+1:N);
         end
end

2. Double Point Crossover

 for i=1:2:Npop
    if(pc > rand())
         index1=round(((N-2)/2)*rand())+1;
         index2=index1+round(((N-2)/2)*rand())+1;
         newpop(i,1:index1)=pop(i,1:index1);
         newpop(i,index1+1:index2)=pop(i+1,index1+1:index2);
         newpop(i,index2+1:N)=pop(i+1,index2+1:N);
         newpop(i+1,1:index1)=pop(i+1,1:index1);
         newpop(i+1,index1+1:index2)=pop(i,index1+1:index2);
	      newpop(i+1,index2+1:N)=pop(i+1,index2+1:N);
     end
 end

V. Mutation The changing and evolution of Data:

for i=1:Npop
      if( pm > rand())
        index1=round((N-1)*rand())+1;
        index2=round((N-1)*rand())+1;
        newpop(i,index1)=1-newpop(i,index1);
        newpop(i,index2)=1-newpop(i,index2);
      end
 end

---

B. Real Case

I. Initial Population: The population is created randomly, consisting of zeros and ones, as follows:

    pop =4*rand(Npop,N)-2;

II. Fitness function
We intent to optimize the module of the chromosome in the population. The activation function is the square of the module of chromosomes:

	function z=Sphere(x)
  	      z=sum(x.^2);
	end
  fitness(i)=1/(1+fitness(i));

III. Selection
Same selection method as the binary case

IV. Crossover The used function is the following:

   for i=1:2:Npop
           if(pc > rand())
               alpha = rand();
                 newpop(i,:)=alpha*pop(i,:)+(1-alpha)*pop(i+1,:);
                 newpop(i+1,:)=alpha*pop(i+1,:)+(1-alpha)*pop(i,:);
            end
   end

V. Mutation The changing and evolution of Data:

where u ∈ N(0,1)

 for i=1:Npop
      if( pm > rand())
          u=randn(1,N);
          newpop(i,:)=newpop(i,:)+sigma.*u;
       end
  end

---

C. Binary-Real Case

I. Initial Population: The population is created randomly, consisting of zeros and ones, as follows: pop =round((2.^n)*rand(Npop,N)-0.5);

II. Fitness function
We intent to optimize the module of the chromosome in the population. The activation function is the square of the module of chromosomes:

	function z=Sphere(x)
  	      z=sum(x.^2);
	end
  fitness(i)=1/(1+fitness(i));

III. Selection
Same selection method as the binary case

IV. Crossover Tt consists in randomly drawing an integer between 1 and N-1 and in exchanging, with a probability Pc.

for i=1:2:Npop
        if(pc > rand())
           indexc1=round((N-1)*rand())+1;
           indexc2=round((N-1)*rand())+1;
             p1 = dectobina(n,pop(i,indexc1));
             p2 = dectobina(n,pop(i+1,indexc2));
             index=round((n-2)*rand())+1;
            newp1(1:index)=p1(1:index);
            newp1(index+1:n)=p2(index+1:n);
            newp2(1:index)=p2(1:index);
            newp2(index+1:n)=p1(index+1:n);        
            newpop(i,indexc1)=bin2deco(newp1);
            newpop(i+1,indexc2)=bin2deco(newp2);
          end
end

V. Mutation The changing and evolution of Data:

for i=1:Npop
      if( pm > rand())
          indexc3=round((N-1)*rand())+1;
        index1=round((n-1)*rand())+1;
         m1 =dectobina(n,newpop(i,indexc3));
           newm1=m1;
           newm1(index1)=1-m1(index1);
           newpop(i,indexc3)=bin2deco(newm1);
      end
end