Difference between revisions of "Local search"
From Adaptive Population based Simplex
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== Basic local search (l0) == | == Basic local search (l0) == | ||
| − | The idea is just to perform a random search "around" | + | The idea is just to perform a random search "around" a good point. So the process is the following: |
* Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population. | * Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population. | ||
* Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below). | * Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below). | ||
Revision as of 18:48, 28 June 2013
Basic local search (l0)
The idea is just to perform a random search "around" a good point. So the process is the following:
- Compute the maximum distance $\rho$ between $x_{best}$ and all the other individuals of the population.
- Select the $x_l$ position at random in the hypersphere of centre $x_{best}$ and of radius $\rho$. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).
If $x_{l}$ is better than $x_i$, decrease the population cost
$$ C\leftarrow C-f(x_i)+f(x_l)$$
If $x_{l}$ is better than the best ever found (i.e. $Best$), set $Best=x_{l}$.
Random choice
The distribution that is used is itself selected at random (uniform distribution) between two ones:
- the uniform one. The components of the direction vector follow the normalised Gaussian distribution, and the radius is $r=\rho*rand(0,1)^{\frac{1}{D}}$
- a non uniform one (more dense near to the centre). Here the radius is simply $r=\rho*rand(0,1)$.
