In the MAXONE problem, we want to maximize the number of ones in a string of...

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In the MAXONE problem, we want to maximize the number of ones in a string of 1 binary digits. The fitness of a candidate solution to the MAXONE problem is the number of ones in its genetic code, the string of 1 binary digits. We start with a population of n random strings. Suppose that 110 and n = 6 and we get the following initial population: sl=1111010101 f(s1)= %f($1)= s2 = 0111000101 f(s2) = %f(s2) $3 = 1110110101 f(83) = %f($3) $4 = 0100010011 f(s4)= %f($4) $5 = 1110111101 f($5)= %f($5) = $6 = 0100110000 f(86) = %f($6) = where f is the fitness function, which associates with every binary string s its fitness f(s). a) Calculate the individual and the total fitness values of the population. By using the roulette wheel method, find the fitness proportions. Sort the strings according to their fitness proportions. Do not take the smallest percentage string. Reuse the one with the largest percentage instead. b) Suppose that the crossover probability is 0.6. Perform crossover only for couples (s1,s3) and (s4,s5). The crossover point is 2 for the first couple and 5 for the second couple. Replace offsprings with the parents in the population. c) Suppose that the mutation probability is 0.1. By using the current population after part b) apply mutation at 6th gene to the first string, 5th and 10th genes to the second string. Replace offsprings with their parents. Calculate the total fitness, is the total fitness of the population improved? In the MAXONE problem, we want to maximize the number of ones in a string of 1 binary digits. The fitness of a candidate solution to the MAXONE problem is the number of ones in its genetic code, the string of 1 binary digits. We start with a population of n random strings. Suppose that 110 and n = 6 and we get the following initial population: sl=1111010101 f(s1)= %f($1)= s2 = 0111000101 f(s2) = %f(s2) $3 = 1110110101 f(83) = %f($3) $4 = 0100010011 f(s4)= %f($4) $5 = 1110111101 f($5)= %f($5) = $6 = 0100110000 f(86) = %f($6) = where f is the fitness function, which associates with every binary string s its fitness f(s). a) Calculate the individual and the total fitness values of the population. By using the roulette wheel method, find the fitness proportions. Sort the strings according to their fitness proportions. Do not take the smallest percentage string. Reuse the one with the largest percentage instead. b) Suppose that the crossover probability is 0.6. Perform crossover only for couples (s1,s3) and (s4,s5). The crossover point is 2 for the first couple and 5 for the second couple. Replace offsprings with the parents in the population. c) Suppose that the mutation probability is 0.1. By using the current population after part b) apply mutation at 6th gene to the first string, 5th and 10th genes to the second string. Replace offsprings with their parents. Calculate the total fitness, is the total fitness of the population improved?