Wheel selection

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.

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. 

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. 

The interferometric measurements with RIfS can be parallelized as demonstrated in Figure 18. In this case, instead of white light interferometry, only a few wavelengths are used to allow parallel detection of all measurement dots. A filter wheel selects one wavelength at a time from the white light source, while the CCD camera monitors the intensity distribution at the transducer for all spots, in this case in a microtiter plate35. 

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. 

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. 

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... 

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. 

A third scheme is called tournament selection. Here, pairs of individuals are selected from the population, and the better of the two enters the breeding pool, whereas the poorer does not. For the SGA, this offers little advantage over roulette wheel selection, but it does allow the population to be replaced incrementally in a clean manner, as discussed next. 

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

Three sets of experimentation have been performed. The first one demonstrates that a tournament selection is better than a roulette wheel selection for an ant colony optimisation algorithm solving high dimensional problems. The second searches for the best number of ants and tournament size for an ant colony optimisation algorithm solving high dimensional problems. The final one explores the potential for T-ACO to operate on lower dimensional problems. 

For 50,000 items as shown in Fig. 7, the tournament selection performs better than the roulette wheel but for 5,000 items Fig. 8 the roulette wheel is better. It shows that a roulette wheel selection is better for smaller sizes of problems. 

In roulette wheel selection, the chance of a parent being selected is directly proportional to its fitness. In the example in Fig. 8.4, from a population of 10 chromosomes with a set of fitness evaluations totalUng 80, 6 individuals are selected by the biased roulette wheel scheme, according to 6 random numbers generated from the interval of 0 and 80. 

In this extremely small population, the individual 11011 is clearly the best performer, but the rule for selection is simply that the greater the fitness of an individual, the more likely it is to be selected. This suggests that even the relatively poor individual 10011 should have some chance, too. The simplest selection scheme is roulette wheel selection. In this scheme, eaeh individual is assigned a... 

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