In a genetic algorithm, a fitness function maps two chromosomes to a fitness value based on the following: for odd numbered positions in a string of 8 values indexed from 1 to 8, the values in odd numbered positions get multiplied by 2 and then summed to obtain f_odd. The numbers of values in even indexed positions get multiplied by 3 then summed to obtain f_even. The fitness value of each chromosome f = f_odd + f_even. Given the following two chromosomes,

{1, 3, 2, 0, 2, 1, 1, 2} and {0, 0, 2, 2, 3, 1, 1, 3}

where the first chromosome is referred to as chromosome 1 and the second as chromosome 2, answer the following questions and clearly indicate your answers.

(1) What is the fitness value of chromosome 1?Answer in whole numbers.

(2) What is the fitness value of chromosome 2? Answer in whole numbers.

(3) Use a cross-over operation to splice the chromosomes between indices 5 and 6 to produce two child chromosomes. When you produce the two child chromosomes, one will have a larger value (in terms of a base 10 number).To indicate both child chromosomes, denote the one with the larger base 10 value to the left of the decimal point, and the one with the smaller base 10 value to the right of the decimal point. For example, if the two chromosomes you produce are 12345678 and 01234567 then indicate these two with the number 12345678.01234567.

(4) Calculate the fitness value for each child chromosome.To indicate the answer, put the larger fitness value to the left of the decimal point and the smaller fitness value to the right of the decimal point.For example, if the two fitness values are 42 and 16 indicate the answer using the number 42.16.

(5) If any of the child chromosomes has a higher or lower fitness value, indicate the fitness value of the child that has a higher fitness value than the parent.