A$)$ Let the populations of chromosomes in genetic algorithm is represented in terms of binary

number. The strength of fitness of a chromosome in decimal form, x is given by

f$($x$)$

$)$

S f $($x$)=$ Ef$($x where f$($x$)=$x$2$

The population is given by P where P$=\{01101),(11000),(01000),(10011)).$ Kindly find the

strength of fitness of chromosome of all the individuals.

B$)$ In a genetic algorithm $($GA$)$ optimization process, roulette wheel selection is a widely used

method for selecting individuals from a population for reproduction based on their fitness

values. Consider a population of candidate solutions represented by binary strings.

$$ Explain how the roulette wheel selection process works in a genetic algorithm, and

discuss its advantages over other selection methods in terms of maintaining diversity

within the population.

$$ Provide a concise explanation of the roulette wheel selection process and highlight

one key advantage it offers in genetic algorithm optimization.