Skip to main content

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.

Comments

Post a Comment

Popular posts from this blog

THE EARTH, A SUPER ORGANISM

     JOIN MY COURSE: "Become a programmer in a day with python"       A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess.      It says, "Earth is a self-regulating organism like a human being.  The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment".  Hence the earth is still suitable for the life to thrive.      Imagine, in a particular place, there are lot of flowers.  Some flowers are white and some are darkly coloured.  We know, white reflects light and heat while dark absorbs the same.  White flowers can thrive in hot climate.  But dark flowers requires cold climate.  The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist.  This is the essence of "Gaia" theory.      On our earth, ...
3 comments
Read more

DISORDER IS THE "ORDER OF THE DAY"

         Imagine a balloon full of air.  The air molecules are moving randomly inside the balloon.  Let us pierce the balloon with a pin.  The air rushes out.  Why should not the air molecules stay inside the balloon safely and ignore the little hole?  That is not the way the world works.  The molecules always "want to occupy as many states as possible".  Hence the air goes out in the open to occupy more volume.   The things always goes into disorder (entropy) and the disorder increases with time.  The above statement is what we call "second law of thermodynamics".      Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze.  Freezing means bringing things to order and arrangement.  It violates the second law.  Hence it will never happen.  Hence heat must flow from high ...
Post a Comment
Read more

CASINO'S GAME

           Let us find out how the casino survives with mathematics.      Say, your friend invite you for a game of dice.  You must bet (wager) 2 dollars.  If you roll 'six' you will get back 8 dollars.  The game will go on for 30 rounds.  All sounds good.      The probability of rolling 'six' is 1/6.  Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5.  That is, you are expected to win 5 rounds out of 30.  Hence your gain will be 5 * 8 =40 dollars.  ok.  This also implies that you will loose 25 rounds.  Hence your loss will be 25*2 =50 dollars.  Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars.  There will be a loss of -1/3 or 0.33 dollars per round.  It is not a fair game.     Let us make a simple formula to calculate  'Pa...
4 comments
Read more