GENETIC WAY TO SOLVE A PROBLEM

 
We grow as an adult; complete our studies; find a good carrier; then select a suitable spouse; get married.  Offsprings get portions of our genes.  They grow as adults….

The story continues generation after generation.  The point here is; the fittest get married and produce off-springs.

This principle can be used to solve a maths problem.
 

f(x) = 3.x-x^2/6.62

The above function yields different results for different values of X.  I want to find a particular value of X for which the function yields maximum.  That is, I want to maximize the function.  Let us assume that X can only take values from 0 to 31.  In a binary system, the range is 00000 to 11111(for the explanation of binary number see note 1)

Let us randomly select six x values in the range 0 to 31 and evaluate the function.

X- decimal	X- binary	f(x) = 3.x-x^2/6.62	selected?
2	00010	5.395	yes
8	01000	14.33	yes
12	01100	14.24	yes
18	10010	5.057	no
22	10110	-7.111	no
28	11100	-34.42	no

Here x values 2, 8, and 12 which yields maximum results are selected.  The corresponding 3 binary values are taken as genes of X.  We are going to mate them and produce six off-springs.  The function will again be evaluated with the off-springs for maximum yield.  

Here mating means, portions of the binary digits are swapped to produce next-generation X as given below.    

I  generation x      II generation x

8    01000             01010   10         

2    00010             00000   0

       Binary or genes, here, colored portions are swapped

I gen. x	Binary or genes	offsprings	II gen. x	f(x)
8	01000	01100	12	14.24
12	01100	01000	8	14.33
8	01000	01010	10	14.82, best
2	00010	00000	0	0
12	01100	01010	10	14.82, best
2	00010	00100	4	9.583

 From the table, we understand X = 10 gives the maximum value of the function 14.82.  Few more runs of this procedure will confirm the result X = 10.  

    

    This method is known as a genetic algorithm in computer parlance.  For complicated problems, the computer will run the algorithm for hundreds of generations and the best result will be taken.  

Note 1: In a binary system, all numbers are represented using only 0 s and 1 s as follows.  (If required, leading zeros can always be added).

2. The following graph of the function proves the result.