# Genetic Algorithms - Tournament Selection

I know this should be a fairly simple concept but I have been Googling a lot and can't seem to find a definitive definition.

If we had the following random population:

[12,2,3,99,73,32,53,8]


And a tournament size of 3. What could be a possible outcome?

Is there lots of variations of Tournament Selection?

A simple version of tournament selection is as follows.

1. Select $k$ random Individuals from the population.
2. Select the best Individual from the $k$ Individuals.
3. Repeat from 1 until you have selected the desired amount of Individuals.

As an example. Consider your data, $k=3$ and that we wish to select 3 Individuals.

$[12,2,3,99,73,32,53,8]$ (your data).

$[12,2,99]$ (3 random Individuals).
$99$ is the best Individual.

$[2,73,53]$ (3 random Individuals).
$73$ is the best Individual.

$[99,8,53]$ (3 random Individuals).
$99$ is the best Individual.

We have selected the Individuals $73,99$ and $99$.

Note that we have selected $99$ twice. If this is not desired, you can delete an Individual from the population if it has been selected.

It is also possible, instead of always selecting the best Individual, to select an Individual according to some stochastic scheme. For example, assign the best Individual from the tournament pool (the $k$ randomly selected individuals) $i=0$, the second best $i=1$, ... (etc), and the worst Individual $i=k-1$. Then Individual $i$ is selected with chance $\frac{2(k-i)}{k(k+1)}$.

I just made this stochastic scheme up. You can use your fantasy on how to extend/alter tournament selection or any other genetic operator :)