Roulette wheel selection

Selection of the fittest

The basic part of the selection process is to stochastically select from one generation to create the basis of the next generation. The requirement is that the fittest individuals have a greater chance of survival than weaker ones. This replicates nature in that fitter individuals will tend to have a better probability of survival and will go forward to form the mating pool for the next generation. Weaker individuals are not without a chance. In nature such individuals may have genetic coding that may prove useful to future generations.

Fig 2. Roulette wheel approach: based on fitness

Example

The normal method used is the roulette wheel (as shown in Figure 2 above). The following table lists a sample population of 5 individuals (a typical population of 400 would be difficult to illustrate).

These individuals consist of 10 bit chromosomes and are being used to optimise a simple mathematical function (we can assume from this example we are trying to find the maximum). If the input range for `x` is between 0 and 10, then we can map the binary chromosomes to base 10 values and then to an input value between 0 and 10.

The fitness values are then taken as the function of `x`. We can see from the table (column `Fitness f(x)`) that individual No. 3 is the fittest and No. 2 is the weakest. Summing these fitness values we can apportion a percentage total of fitness. This gives the strongest individual a value of 38% and the weakest 5%.

These percentage fitness values can then be used to configure the roulette wheel. Figure 2 highlights that individual No. 3 has a segment equal to 38% of the area.

The number of times the roulette wheel is spun is equal to size of the population. As can be seen from the way the wheel is now divided, each time the wheel stops this gives the fitter individuals the greatest chance of being selected for the next generation and subsequent mating pool.

What is possibly more interesting from this example is that as the generations progress and the population gets fitter the gene pattern for individual No. 3: `01000001012` will become more prevalent in the general population because it is fitter, more apt to the environment we have put it in - in this case the function we are trying to optimise.

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