Difference between revisions of "Local search"
From Adaptive Population based Simplex
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=== Random choice === | === Random choice === | ||
The distribution that is used is itself selected at random (uniform distribution) between two ones: | 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}} | + | # 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=ρ∗rand(0,1). | # a non uniform one (more dense near to the centre). Here the radius is simply r=ρ∗rand(0,1). | ||
Revision as of 19:13, 28 June 2013
Basic local search (l0)
The idea is just to perform a random search "around" the current best point. So the process is the following:
- Compute the maximum distance ρ between xbest and all the other individuals of the population.
- Select the xl position at random in the hypersphere of centre xbest and of radius ρ. The basic random choice makes use of two distributions, an uniform one, and a non-uniform one (see below).
If xl is better than xi, decrease the population cost
C←C−f(xi)+f(xl)
If xl is better than the best ever found (i.e. Best), set Best=xl.
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=ρ∗rand(0,1)1/D
- a non uniform one (more dense near to the centre). Here the radius is simply r=ρ∗rand(0,1).
