Difference between revisions of "Initialisation"
From Adaptive Population based Simplex
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| − | == Basic | + | == Basic initialisation (i0) == |
| − | + | [[Image:Basic APS N vs D.png|right|thumb|400px|Population size vs Dimension]] | |
Draw at random $N$ agents (positions) in the search space, according to an uniform distribution. | Draw at random $N$ agents (positions) in the search space, according to an uniform distribution. | ||
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where $D$ is the dimension of the search space. Note that $N$ needs to be at least equal to $D+1$. | where $D$ is the dimension of the search space. Note that $N$ needs to be at least equal to $D+1$. | ||
| − | + | We will need the volume $V(0)$ of the previous simplex. As no one has been defined yet, we simply set it to 0:<br /> | |
| + | $$V(0)=0$$ | ||
| + | |||
| + | === Population cost === | ||
| + | Evaluate the $N$ individuals, thanks to the function $f$ we are studying. Save the best one as $Best$. | ||
| + | |||
| + | The sum of all values (they are all supposed to be positive, which is always possible), is the initial ''population cost'' $C$. We are trying here to minimise it. | ||
Latest revision as of 17:55, 28 June 2013
Basic initialisation (i0)
Draw at random $N$ agents (positions) in the search space, according to an uniform distribution.
$N=\max\left(40+2\sqrt{D},\sqrt{40^{2}+\left(D+2\right)^{2}}\right)\tag{1}$
where $D$ is the dimension of the search space. Note that $N$ needs to be at least equal to $D+1$.
We will need the volume $V(0)$ of the previous simplex. As no one has been defined yet, we simply set it to 0:
$$V(0)=0$$
Population cost
Evaluate the $N$ individuals, thanks to the function $f$ we are studying. Save the best one as $Best$.
The sum of all values (they are all supposed to be positive, which is always possible), is the initial population cost $C$. We are trying here to minimise it.
