# IX. Selection

### Introduction

As you already know from the GA outline, chromosomes are selected from the population to be parents for crossover. The problem is how to select these chromosomes. According to Darwin's theory of evolution the best ones survive to create new offspring. There are many methods in selecting the best chromosomes. Examples are roulette wheel selection, Boltzman selection, tournament selection, rank selection, steady state selection and some others.

Some of them will be described in this chapter.

### Roulette Wheel Selection

Parents are selected according to their fitness. The better the chromosomes are, the more chances to be selected they have. Imagine a roulette wheel where all the chromosomes in the population are placed. The size of the section in the roulete wheel is proportional to the value of the fitness function of every chromosome - the bigger the value is, the larger the section is. See the following picture for an example.

A marble is thrown in the roulette wheel and the chromosome where it stops is selected. Clearly, the chromosomes with bigger fitness value will be selected more times.

This process can be described by the following algorithm.

1. [Sum] Calculate the sum of all chromosome fitnesses in population - sum S.
2. [Select] Generate random number from the interval (0,S) - r.
3. [Loop] Go through the population and sum the fitnesses from 0 - sum s. When the sum s is greater then r, stop and return the chromosome where you are.

Of course, the step 1 is performed only once for each population.

### Rank Selection

The previous type of selection will have problems when they are big differences between the fitness values. For example, if the best chromosome fitness is 90% of the sum of all fitnesses then the other chromosomes will have very few chances to be selected.

Rank selection ranks the population first and then every chromosome receives fitness value determined by this ranking. The worst will have the fitness 1, the second worst 2 etc. and the best will have fitness N (number of chromosomes in population).

You can see in following picture, how the situation changes after changing fitness to the numbers determined by the ranking.

Situation before ranking (graph of fitnesses)

Situation after ranking (graph of order numbers)

Now all the chromosomes have a chance to be selected. However this method can lead to slower convergence, because the best chromosomes do not differ so much from other ones.

This is not a particular method of selecting parents. The main idea of this type of selecting to the new population is that a big part of chromosomes can survive to next generation.

The stady-state selection GA works in the following way. In every generation a few good (with higher fitness) chromosomes are selected for creating new offspring. Then some bad (with lower fitness) chromosomes are removed and the new offspring is placed in their place. The rest of population survives to new generation.

### Elitism

The idea of the elitism has been already introduced. When creating a new population by crossover and mutation, we have a big chance, that we will loose the best chromosome.

Elitism is the name of the method that first copies the best chromosome (or few best chromosomes) to the new population. The rest of the population is constructed in ways described above. Elitism can rapidly increase the performance of GA, because it prevents a loss of the best found solution.

(c) Marek Obitko, 1998