**2.2.2 Stochastic universal sampling**

84 Advanced Topics in Measurements

1. The fitness function is evaluated for each individual, providing fitness values, which are then normalized. Normalization means dividing the fitness value of each individual by the sum of all fitness values, so that the sum of all resulting fitness values equals 1.

3. Accumulated normalized fitness values are computed (the accumulated fitness value of an individual is the sum of its own fitness value plus the fitness values of all the previous individuals). The accumulated fitness of the last individual should be 1

5. The selected individual is the first one whose accumulated normalized value is greater

Retaining the best individuals in a generation unchanged in the next generation, is called elitism or elitist selection. It is a successful (slight) variant of the general process of

Fitness proportionate selection, also known as roulette-wheel selection, is a genetic operator used in genetic algorithms for selecting potentially useful solutions for recombination.

In fitness proportionate selection, as in all selection methods, the fitness function assigns a value to possible solutions or chromosomes. This fitness level is used to associate a probability of selection with each individual chromosome. If *<sup>i</sup> f* is the fitness of individual *i*

This could be imagined similar to a Roulette wheel in a casino. Usually a proportion of the wheel is assigned to each of the possible selection based on their fitness value. This could be achieved by dividing the fitness of a selection by the total fitness of all the selections, thereby normalizing them to 1. Then a random selection is made similar to how the roulette wheel is

While candidate solutions with a higher fitness will be less likely to be eliminated, there is still a chance that they may be. Contrast this with a less sophisticated selection algorithm, such as truncation selection, which will eliminate a fixed percentage of the weakest candidates. With fitness proportionate selection there is a chance some weaker solutions may survive the selection process; this is an advantage, as though a solution may be weak, it may include some

The analogy to a roulette wheel can be envisaged by imagining a roulette wheel in which each candidate solution represents a pocket on the wheel; the size of the pockets are proportionate to the probability of selection of the solution. Selecting *N* chromosomes from the population is equivalent to playing *N* games on the roulette wheel, as each candidate is

, where *N* is the number of individuals in the

*i N j j*

component which could prove useful following the recombination process.

*f <sup>p</sup> <sup>f</sup>*

A generic selection procedure may be implemented as follows:

2. The population is sorted by descending fitness values.

4. A random number R between 0 and 1 is chosen.

than R.

population.

rotated.

drawn independently.

constructing a new population.

**2.2.1 Roulette-wheel selection** 

its probability of being selected is *<sup>i</sup>*

(otherwise something went wrong in the normalization step).

Stochastic universal sampling (SUS) is a technique used in genetic algorithms for selecting potentially useful solutions for recombination. It was introduced by James Baker.

SUS is a development of fitness proportionate selection which exhibits no bias and minimal spread. Where fitness proportionate selection chooses several solutions from the population by repeated random sampling, SUS uses a single random value to sample all of the solutions by choosing them at evenly spaced intervals.

While candidate solutions with a higher fitness will be less likely to be eliminated, there is still a chance that they may be. Contrast this with a less sophisticated selection algorithm, such as truncation selection, which will eliminate a fixed percentage of the weakest candidates. With fitness proportionate selection there is a chance some weaker solutions may survive the selection process; this is an advantage, as though a solution may be weak, it may include some component which could prove useful following the recombination process.

The analogy to a roulette wheel can be envisaged by imagining a roulette wheel in which each candidate solution represents a pocket on the wheel; the size of the pockets are proportionate to the probability of selection of the solution. Selecting *N* chromosomes from the population is equivalent to playing *N* games on the roulette wheel, as each candidate is drawn independently.
