Difference between revisions of "Local search"

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m (Random choice)
m (Basic local search (l0))
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== Basic local search (l0) ==
 
== Basic local search (l0) ==
The idea is just to perform a random search "around" the current best point. So the process is the following:
+
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:

  1. the uniform one. The components of the direction vector follow the normalised Gaussian distribution, and the radius is $r=\rho*rand(0,1)^{\frac{1}{D}}$
  2. a non uniform one (more dense near to the centre). Here the radius is simply $r=\rho*rand(0,1)$.