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Holland's original GA used fitness-proportionate selection, in which the expected value of an individual (i.e., the expected number of times an individual will be selected to reproduce) is that individual's fitness divided by the average fitness of the population. The most common method for implementing this is roulette wheel sampling, described in chapter 1 each individual is assigned a slice of a circular roulette wheel, the size of the slice being proportional to the individual's fitness. The wheel is spun N times, where N is the number of individuals in the population. On each spin, the individual under the wheel's marker is selected to be in the pool of parents for the next generation. This method can be implemented as follows This stochastic method statistically results in the expected number of offspring for each individual. However, with the relatively small populations typically used in GAs, the actual number of offspring allocated to an individual is often far from its...
Implement SUS and use it on the fitness function described in computer exercise 1 in chapter 1. How does this GA differ in behavior from the original one with roulette-wheel selection Measure the spread (the range of possible actual number of offspring, given an expected number of offspring) of both sampling methods.
A simple method of implementing fitness-proportionate selection is roulette-wheel sampling (Goldberg 1989a), which is conceptually equivalent to giving each individual a slice of a circular roulette wheel equal in area to the individual's fitness. The roulette wheel is spun, the ball comes to rest on one wedge-shaped slice, and the corresponding individual is selected. In the n 4 example above, the roulette wheel would be spun four times the first two spins might choose chromosomes B and D to be parents, and the second two spins might choose chromosomes B and C to be parents. (The fact that A might not be selected is just the luck of the draw. If the roulette wheel were spun many times, the average results would be closer to the expected values.)
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