Roulette wheel selection procedure

Roulette wheel selection In this selection variant the probability for selecting a chromosome is proportional to its fitness. The idea can be illustrated when we imagine a roulette wheel, where a slot is allocated to each chromosome and the size of the slot is chosen with respect to the quality of the chromosome. When the wheel is spinning the chromosomes with a better quality are more likely to be chosen than those of a minor quality. Figure 9-28 illustrates this procedure,... 

The wheel is spun and the string into whose slot the virtual ball falls is copied once into the parent pool. This procedure is repeated npop times to pick the full complement of parent strings. In roulette wheel selection, every string has a nonzero chance of being picked, proportional to its fitness, so even the poorest string may be chosen as a parent. The method also preferentially selects the fitter strings and, because of these features and its simplicity, roulette wheel selection is widely used. 

Conversely, a crossover operator is used based on confidence intervals. This operator uses information from the best individuals in the population. Moreover, the crossover operator is associated with the capacity of interpolation (exploration). This capacity is related to the belonging of a population parameter to a confidence interval. The crossover operator is also associated with the capacity of extrapolation (exploitation). To select the suitable parents for the next generation, the roulette wheel selection method is used. This method consists of a random selection in which the best quality individuals have more possibilities to be selected. In this way, the explained operators create new individuals that are added to the population. To produce the next generation, that extended population is reduced to its original size using the rank-space method. This selection procedure links fitness to both quality rank and diversity rank. Thus, it promotes not only the survival of individuals, which are extremely fit from the perspective of quality, but also the survival of those that are both quite fit and different from others. 

The genetic crossover operator adopted here is the k-point crossover. The mutation operator is based on a random sort of a procedure to guarantee the diversity of the explored solutions (random gene replacement, gene permutation. ..). The classical Goldberg s biased roulette wheel is used for selection. 

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