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).
