a) Consider 10 Boolean variables, Bi, i = 1, 2, ....., 10. Each variable assumes the

value T (true) or F(false). Next, consider the following four expressions :

i)

B2 or B7

ii)

iii)

(B1 and B3) or (B4 and B8 and B10) and B6

(B1 or B3 and B4) or (B5)

(B2 and B5) and (B1 and B4 or B6)

iv)

Use Genetic algorithm to assign a solution to each Boolean variable that maximizes the number of false logical expressions. Carry

out five iterations. Select the best two parents from population size = 5 for 2-point crossover to create two offspring. Use random

number to mutate two offspring. Replace two worst solutions by two offsprings for the next iteration.

(6M)

b)

Apply the random walk heuristic to estimate the minimal solution of the

following two-variable function:

f(x)= 5x2 - 3y2 + 2xy ,0 sxs 8,0 sy s 5,

Assume that

Xo = 0.5, yo = 0.3 and XK+1 = X45(Rx - 0.5), yk+1 = yk+ 5(R) - 0.5)

(4M)