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
    • 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?

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