- Discuss whether there is survival of the fittest in a

generational EA.
- Given the fitness function f(x) = x
^{2}, calculate selection probabilities for Fitness Proportional Selection for the individuals x=1, x=2, x=3.
- For the same individuals, calculate the selection probabilities for a transposed fitness function f'(x) = f(x) + 100.
- 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?

- You are given the fitness function f(x) = x
^{2} +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).

- Calculate the probabilities of selecting b via fitness proportionate selection if the new fitness function is f'(x) = x
^{2}
- 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?

## The on-line accompaniment to the book Introduction to Evolutionary Computing