Question

Suppose a genetic algorithm uses chromosomes of the form (x = abcdefgh) with a fixed length of 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),

Initial population consist of four with the following chromosomes:

x1 = 6 5 4 1 3 5 3 2

x2 = 8 7 1 2 6 6 0 1

x3 = 2 3 9 2 1 2 8 5

x4 = 4 1 8 5 2 0 9 4

(a) Evaluate the fitness of each, show in descending order

(b) Do one-point cross over of 2 fittest individuals at midpoint

(c) Do 2 points crossover (b, f) of second and third fittest

(d) Cross the 1st and 3rd using a uniform cross over

(e) New population now consists of the six offsprings. Evaluate the fitness. Has the overall fitness improved?

(f) Considering that genes can only be digits between 0 and 9 find the chromosome representing the optimal solution. Find the value of the maximum fitness.

(g) Can you say whether it will be able to reach the optimal solution without the mutation operator?

Answer 1

As the question contains more than 4 parts so I would be solving the 1st 4 parts of the question only(following the guidelines of Chegg):-