# Exercises for Chapter Five: Fitness, Selection, and Population Management

1. Discuss whether there is survival of the fittest in a
generational EA.
2. Given the fitness function f(x) = x2, calculate selection probabilities for Fitness Proportional Selection for the individuals x=1, x=2, x=3.
3. For the same individuals, calculate the selection probabilities for a transposed fitness function f'(x) = f(x) + 100.
4. A generational EA has a population size of 100, uses
fitness proportionate selection without elitism, and after t
generations has a mean population fitness of 76.0. There is one
copy of the current best member, which has fitness 157.0.

• What is the expectation for the number of copies of the
best individual present in the mating pool?
• What is the probability that there will be no
copies of that individual in the mating pool, if
selection is implemented using the roulette wheel
algorithm?
• What is the probability if the implementation uses SUS?
5. You are given the fitness function f(x) = x2 +10 and a population of three individuals {a,b,c}. When decoded their genes when decoded give the values 1, 2 and 3 respectively. When you pick a single parent using Fitness Proportionate Selection, what is the probability that it is b?
• 14/(11+14+19).
• 1/3.
• 2/3.
• 14 /(11+12+13).
• 14/(1+2+3).
6. Calculate the probabilities of selecting b via fitness proportionate selection if the new fitness function is f'(x) = x2
7. What is the probability of selecting b via binary tournament selection for the example above? How does it change when the fitness function has it’s values reduced by 10?