. Q2 Genetic Algorithm Suppose a genetic algorithm uses chromosomes of the form x - abcdefgh with a fixed lengthof eig

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. Q2 Genetic Algorithm
Suppose a genetic algorithm uses chromosomes of the form x - abcdefgh with a fixed lengthof eight genes . Each gene can be any digit between 0 and 9. Let the fitness of individual x be calculated as f ( x ) = ( a + b ) ( c + d ) + ( e + f ) - ( g + h ) . and let the initial population consist of four individuals with the following chromosomes

xl =65413532
x=87126601
x3=23921285
x4=41852094
a.Evaluate the fitness of each individual , showing all your workings , and arrange them in order with the fittest first and the least fit last
b . Perform the following crossover operations :
i ) Cross the fittest two individuals using one - point crossover at the middle point .
ii ) Cross the second and third fittest individuals using a two - point crossover ( point b and f)
iii ) Cross the first and third fittest individuals ( ranked 1st and 3rd ) using a uniform crossover
c ) Suppose the new population consists of the six offspring individuals received by the crossover operations in the above question . Evaluate the fitness of the new population , showing all your workings . Has the overall fitness improved ?
d ) By looking at the fitness function and considering that genes can only be digits between 0 and 9 find the chromosome representing the optimal solution ( i.e. with the maximum fitness ) . Find the value of the maximum fitness .