Difference between revisions of "Selection"
From Adaptive Population based Simplex
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== Basic selection (s0) == | == 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 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. | # Select the three first ones. | ||
# Sort them, by increasing order of value (fitness). They are $x_{best}$, $x_{worst2}$, and $w_{worst}$. | # 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 $Best=x_{best}$. | If $x_{best}$ is better than the best ever found (i.e. $Best$), set $Best=x_{best}$. | ||
| + | |||
| + | === Adaptive probability === | ||
| + | The rationale is the following:<br /> | ||
| + | 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. | ||
Latest revision as of 17:15, 28 June 2013
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.
