IGNOU MMTE 7 2026 - Verify whether the Genetic Algorithm (GA) improves the solution from o

Question

Verify whether the Genetic Algorithm (GA) improves the solution from one generation to the next generation, for the function given below:
Maximize:

$$f(x) = \sqrt{x}$
Subject to:

$$1 \le x \le 16$
Assume that chromosomes of length 6 are created at random and modified by Roulette-Wheel selection.

10 Jan 2026

Answer :

Word Count : 307

The variable (x) is represented by a 6-bit binary chromosome. A 6-bit string can represent integers from 0 to 63. To map this to the feasible range (1 \le x \le 16), linear decoding is used: [ x = 1 + \frac{\text{decimal value of chromosome}}{63},(16-1) ] Initial population (Generation 0) is assumed random with four chromosomes. [ \begin{array}{c|c|c|c} \text{Chromosome} & \text{Decimal} & x & f(x)=\sqrt{x} \ \hline 010011 & 19 & 1 + \frac{19}{63}\cdot 15 = 5.52 & 2.35 \ 101000 & 40 & 1 + \frac{40}{63}\cdot 15 = 10.52 & 3.24 \ 001101 & 13 & 1 + \frac{13}{63}\cdot 15 = 4.10 &

__________ _____ ____ __________ _____.
_________ _______ ___ ____ ______ ____ _____.
__________ _______ __________ ________ ________ _____ __________ _________.
________ ________ __________ ____ __________ _________ _______ _______ ________ _________.
________ _____ ____ _______ ___ ___.
______ __________ _________ ___ ______ ______ _______.
___ __________ _____ ____ _______ ________ _____ _____ ___ _________ __________ _____.
_______ _______ ____ ___ _________ ______ ________.
___ ___ _______ ______ ______ _________ _____ _______ _________ ___.
________ _____ _________ ___ _____.
________ ____ _____ _________ _________ ___ ______.
___ ________ __________ ___ ______ ____ ____ ______ _________ _____.
_______ ______ __________ __________ ___ _________.
_________ ______ ______ ____ _____ ____ _______ ____.
______ ___ _________ __________ _________ ___ ____ _______ _____ _____.
____ _________ _______ _______ _________ ___.
______ _______ ________ ________ __________ ___ _______.
___ _______ _______ _____ _____.
_____ ______ _____ ____ _____ ___ ___.
________ __________ _________ ____ ________ ________ _____ ____.
________ ________ ________ ____ _____ _____ ____ ____.
_________ ________ ________ _________ ____ _______ ___.
______ __________ ___ __________ ____ ____ __________ ________ ______.
___ ________ ________ ____ _______ ________ ___ _________ ________.
____ ____ _____ _______ ________ ________ _________ ____ ____ ________ ______ ______.
___ ______ _______ __________ _________.
________ _________.

IGNOU ACADEMY

Your IGNOU journey, made easier.