# Selection

From Adaptive Population based Simplex

## Basic selection (s0)

- Select a simplex $S$ (i.e. $D+1$ individuals) at random. Be sure that the current one is in this list. If not, replace the last of the list by the current one.
- Select the three first ones.
- Sort them, by increasing order of value (fitness). They are $x_{best}$, $x_{worst2}$, and $w_{worst}$.

If $x_{best}$ is better than the best ever found (i.e. $Best$), set $Best=x_{best}$.

### Adaptive probability

The rationale is the following:

the more the simplex volume increases, the less the algorithm is successful, and the more one needs randomness to increase the diversity.

Compute the volume $V(1)$ of the simplex. If the previous volume is zero (in practice, too small) the probability $p$ is set to 0.5. If not, the formula is $$ p=\frac{1}{1+e^{-\frac{V(1)-V(0)}{V(0)}}} $$

After that, we simply set $V(0)=V(1)$, to save the simplex volume as the "previous" one.