Roulette wheel selection

Keywords Subset-based ant colony optimisation High dimensional NP-hard problems Tournament selection Roulette wheel selection Knapsack problem... 

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,... 

Figure 9-28. Roulette wheel selection. The size of each sector is equivalent to the fitness of the corresponding chro iTiosoiTie.

In roulette wheel (or dartboard) selection, each string in the population is allocated a segment on a virtual roulette wheel (dartboard) of a size proportional to the string s fitness (Figure 5.17). 

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. 

A weakness of both roulette wheel selection and tournament selection is that although both are biased in favor of fitter strings as the algorithm requires, neither guarantees that the best string in one generation will be chosen as a parent for the next. 

The ball might never fall into the widest slot in the roulette wheel. In fact, it is possible, though unlikely, that the roulette wheel will select only the poorest strings from a population to act as parents. Tournament selection cannot select the worst string, but it is only able to choose the best string from among... 

Roulette wheel selection. The area of the slot on the virtual roulette wheel for each string is proportional to the string s fitness. 

Run roulette wheel selection on the residual fitnesses to fill any remaining places in the parents pool, reducing the residual fitness to zero for any string as soon as it is selected to be a parent in this process. 

We shall use roulette wheel selection. Spinning the virtual wheel ten times gives us ten strings as the starting point for the new population (Table 2). We note that the fitter strings are indeed now more numerous than before, as we would expect, although, as there is a stochastic element in the choice of parents, repeated runs on the same problem can be expected to generate different results. 

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. 

A variety of methods have been proposed for the selection step. One of the earliest, and most straightforward, is the roulette wheel, in which the probability of a string being chosen, is proportional to the fraction of the total fitness of the... 

On the roulette wheel, each string is allocated a segment whose size is proportional to the string s fitness (Fig. 10). The wheel is spun, and the string into whose slot the imaginary roulette ball falls is selected to be copied once into the new population. The process is repeated until the new population is equal in size to the starting population. 

The GA parameters are as follows population size = 20 fraction of population to keep = 0.5 mutation rate = 0.3 Roulette wheel selection and two point crossover method. 

The actual methodology used for this is the roulette wheel selection. We divide the range of random number, R, into Np zones 0 < / < Pj ... 

In this step, a selection method is used in order to fill the mating pool, P(t-tl)). A variety of selection methods can be used in EAs. Two classical selection schemes are the roulette wheel selection and the tournament selection. In the first scheme, chromosomes are chosen according to a given probability, which is a function of their fitness . In the second scheme, a number of chromosomes are randomly chosen from the previous generation. 

In our MOEA methodology, we use a combination of roulette wheel and tournament selection approaches according to ... 

Fig 9 21 The basis of roulette wheel selection shmoing how the more fit members of the population are selec ted in proportion to their fitness values... 

Select individuals for the next generation with a probability proportional to the fitness value from a roulette wheel on which the slot size is proportional to the fitness value. Notice that genetic algorithms use probabilistic, not deterministic, transition rules. 

Figure 2 An illustration of the roulette wheel used for selecting individuals for mating. The fraction of the circle allotted to an individual is proportional to the individual s fitness.

One of the dangers of roulette wheel selection is that if a single individual is much more fit than any other in the population, then it can completely take over the population. This causes the GA to converge prematurely. Once the mating pool is produced, the next generation is created with replacement and crossover operators. It is worth reiterating that the SGA uses a constant population size that is specified at the beginning of the calculation. Replacement and crossover terminate when this number of individuals have been created for the new population. 

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