Introduction :
Hi every .. this article is about Genetic search algorithm ... in general, it's used to find a maximum or minimum value of a given function using the concept of biological chromes and genes.
Basics :
So for now ... what we need to do ... is to make 2 population set ... where a current set have the initial points ( chromes ) , and the next set containing the points ( chromes ) produced by the first set .... and so on ... untill we finish the no. of iterations.
i.e: Current set for randomly initialised chromes :
current population of 4 chromes,
* each row is a chrome.
* each chrom consist of 6 genes ( 6 columns ) [ 1 sign bit and 5 other bits ] and a fitness value [the last column to the right] that represent the function value y(x) at the value of the given chrom (x) ... where the chrom is converted to an integer value from the bits conversion ...
|
c no. |
Sb |
b5 |
b4 |
b3 |
b2 |
b1 |
fit |
|
1 |
0 |
1 |
0 |
1 |
1 |
0 |
8 |
|
2 |
1 |
0 |
0 |
1 |
0 |
0 |
6 |
|
3 |
0 |
0 |
1 |
0 |
1 |
0 |
9 |
|
4 |
0 |
0 |
0 |
1 |
1 |
0 |
12 |
Functions :
1- Picking the best chromes :
as in the actual life principles ... " Survival is for the strongest " , so we choose the best 2 elements of the set ( current population ) according to their fitness ( highest fitness as we are looking for a the maximum value of the function ).
the new set:
|
c no. |
Sb |
b5 |
b4 |
b3 |
b2 |
b1 |
fit |
|
4 |
0 |
0 |
0 |
1 |
1 |
0 |
12 |
|
3 |
0 |
0 |
1 |
0 |
1 |
0 |
9 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2- Cross over to generate the children :
so now in the new set we have the two chromes picked from the old set ... they are parents to the other two chromes in the set whom will be generated by crossing over the two chromes at a certain point and exchange the two parts as follows :
Cross over occured after bit 3 ( notice the bold and the italic digits being crossed in the children from the parents )
|
c no. |
Sb |
b5 |
b4 |
b3 |
b2 |
b1 |
fit |
|
4 |
0 |
0 |
0 |
1 |
1 |
0 |
12 |
|
3 |
0 |
0 |
1 |
0 |
1 |
0 |
9 |
|
child 1 |
0 |
0 |
0 |
0 |
1 |
0 |
14 |
|
child 2 |
0 |
0 |
1 |
1 |
1 |
0 |
5 |
3- Mutation with a low probability :
Mutation occurs with a low probability in one chrome in the set... by inverting a one of the bits in the chrom.
4- loop termination :
now we have the new set ... so we make the old set equal to the new one ... and do the 1,2,and 3 again depending on the no. of iterations.
Step by step coding :
#include<stdio.h> //to use the printf function
#include<conio.h> //to use the getche function
#include<stdlib.h> //to use the rand function
typedef struct Chrom // creating the chrom structure
{
short int bit[6];
int fit;
}chrom; // now we have a chrom type that we can use
void *evpop(chrom popcurrent[4]); //defining the functions that we will use
int x(chrom popcurrent);
int y(int x);
void *pickchroms(chrom popcurrent[4]);
void *crossover(chrom popnext[4]);
void *mutation(chrom popnext[4]);
void main() // the main function
{
int num; // num is the no. of iterations
int i,j;
printf("\nWelcome to the Genetic Algorithm coded by Luay Al-wesi : www.luay.info \nThe Algorithm is based on the function y = -x^2 + 5 to find the maximum value of the function...\n"); // introduction to the program
enter: printf("\nPlease enter the no. of iterations: ");
scanf("%d",&num); // enter the no. of iterations in num
chrom popcurrent[4]; // we make 4 chromes of popcurrent
chrom popnext[4]; // we make 4 chromes of popnext
if(num<1) // if a -ve number is inserted .. enter num again
goto enter;
evpop(popcurrent); //initialise pop current
for(i=0;i<num;i++) // loop num times
{
printf("\ni = %d\n",i); // print the iteration number
for(j=0;j<4;j++)
popnext[j]=popcurrent[j]; //copy popcurrent to popnext in order to adjust it
pickchroms(popnext); //pick best chromes
crossover(popnext); //cross over to get children chromes
mutation(popnext); //mutate with a low probability
for(j=0;j<4;j++)
popcurrent[j]=popnext[j]; //copy the chromes of popnext to popcurrent
} // loop back until no. of iterations is exceeded
printf("\nPress any key to end ! ");
flushall(); // flush the input buffer
getche(); // wait for a character from the keyboard to end
} //end of main
void *evpop(chrom popcurrent[4]) //takes a pointer to a chrom of 4 elements
{
int i,j,value;
int random;
for(j=0;j<4;j++) // loop of j to choose chromes from [0] to [3]
{
for(i=0;i<6;i++) // loop of i to choose the gen of the chrom from [0] to [5]
{
random=rand(); // creating random value
random=(random%2); // make the random value o or 1 only
popcurrent[j].bit[i]=random; // initialising the bit[i] of chrom[j] with random
} // end of for(i)
value=x(popcurrent[j]); // get the value of the chrom as integer
popcurrent[j].fit=y(x(popcurrent[j])); // calcualte the fitness of chrom[j]
printf("\n popcurrent[%d]=%d%d%d%d%d%d value=%d fitness = %d",j,popcurrent[j].bit[5],popcurrent[j].bit[4],popcurrent[j].bit[3],popcurrent[j].bit[2],popcurrent[j].bit[1],popcurrent[j].bit[0],value,popcurrent[j].fit); // print the chrom[j]
} // end of for(j)
return(0);
} //end of evpop function
int x(chrom popcurrent) //x function that evaluate the value of a given chrom
{
int z;
z=(popcurrent.bit[0]*1)+(popcurrent.bit[1]*2)+(popcurrent.bit[2]*4)+(popcurrent.bit[3]*8)+(popcurrent.bit[4]*16);
if(popcurrent.bit[5]==1)
z=z*(-1); // z=sum of the ( bits * their weights) with the sign value
return(z); //return the value of z
} // end x function
int y(int x) // the y function that we look for it's maximum value takes x value
{
int y;
y=-(x*x)+5; // the function is y= - ( x^ 2 ) +5
return(y);
} // end of y function
void *pickchroms(chrom popcurrent[4]) // pickchroms takes a pointer to array of chroms
{
int i,j;
chrom temp; //temp chrome to use in sorting
for(i=0;i<3;i++) //sorting the given set due to fitness
for(j=0;j<3;j++)
{
if(popcurrent[j+1].fit>popcurrent[j].fit)
{
temp=popcurrent[j+1];
popcurrent[j+1]=popcurrent[j];
popcurrent[j]=temp;
} // end of if
} // end of for loop
for(i=0;i<4;i++)
printf("\nSorting:popnext[%d] fitness=%d",i,popcurrent[i].fit); //printing the result
printf("\n"); //print new line
flushall(); //flush the input buffer
return(0);
} //end of pick chromes function
void *crossover(chrom popnext[4]) // crossover function takes a pointer to array of chromes
{
int random;
int i;
random=rand(); //random cross over point
random=((random%5)+1); // cross point should be between (1 - 5)
for(i=0;i<random;i++) //crossing the bits below the cross point index
{
popnext[2].bit[i]=popnext[0].bit[i]; //child 1 cross over
popnext[3].bit[i]=popnext[1].bit[i]; // child 2 cross over
} // end of for
for(i=random;i<6;i++) // crossing the bits beyond the cross point index
{
popnext[2].bit[i]=popnext[1].bit[i]; // child 1 cross over
popnext[3].bit[i]=popnext[0].bit[i]; // chlid 2 cross over
} // end of for
for(i=0;i<4;i++)
popnext[i].fit=y(x(popnext[i])); // calculating the fitness values for the new set
for(i=0;i<4;i++)
printf("\nCrossOver popnext[%d]=%d%d%d%d%d%d value=%d fitness = %d",i,popnext[i].bit[5],popnext[i].bit[4],popnext[i].bit[3],popnext[i].bit[2],popnext[i].bit[1],popnext[i].bit[0],x(popnext[i]),popnext[i].fit);
// printing the bits, value and fitness for the chromes of the new set
return(0);
} // end crossover function
void *mutation(chrom popnext[4]) // mutation funtion given a pointer to array of chromes
{
int random;
int row,col,value;
random=rand()%50; //random value is between ( 0 - 49 )
if (random==25) // Suppusiong Probability of mutation is 2 %
{
col=rand()%6; // random column (gene) choosing
row=rand()%4; // random row ( chrome ) choosing
if (popnext[row].bit[col]==0) // invert the bit to 1 if it was 0
popnext[row].bit[col]=1 ;
else if (popnext[row].bit[col]==1) // invert the bit to 0 if it was 1
popnext[row].bit[col]=0;
popnext[row].fit=y(x(popnext[row])); // calculate the fitness for the mutated chrome
value=x(popnext[row]);
printf("\nMutation occured in popnext[%d] bit[%d]:=%d%d%d%d%d%d value=%d fitness=%d",row,col,popnext[row].bit[5],popnext[row].bit[4],popnext[row].bit[3],popnext[row].bit[2],popnext[row].bit[1],popnext[row].bit[0],value,popnext[row].fit);
// print the chrome index,bits,value, fintness of the mutated chrome
} // end of if
return(0);
} //end of mutation
Finally
hope you benefit from this code ...
god bless
