Difference between revisions of "Local search"
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(Created page with "TO COMPLETE == Basic local search (l0) == Define a hypersphere around the best point of the three ones defined in the selection phase.<br /> Radius= maximum distance to the o...") |
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== Basic local search (l0) == | == Basic local search (l0) == | ||
| − | + | The idea is to perform a random search "around" a good point, but only if the current point is worse than average, i.e. if $\frac{f(x_i)}{N}>C$. In that case, 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). | ||
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| + | If $x_{l}$ is better than $x_i$, decrease the population cost | ||
| + | $$ C\leftarrow C-f(x_i)+f(x_l)$$ | ||
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| + | If $x_{l}$ is better than the best ever found (i.e. $Best$), set $Best=x_{l}$. | ||
| − | The | + | === 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 $r=\rho*rand(0,1)$. | ||
Latest revision as of 09:06, 22 September 2015
Basic local search (l0)
The idea is to perform a random search "around" a good point, but only if the current point is worse than average, i.e. if $\frac{f(x_i)}{N}>C$. In that case, 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 $r=\rho*rand(0,1)$.
