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3.4.1 Simulated Annealing
Consider a Metropolis walk through the space of ``states''
with
where
is a ``cost function'' to be
minimized, and a tunable parameter (a reciprocal
``temperature''.)
- Low
smaller variation of ;
higher
are accessible
- High
will tend to go ``downhill''
EXERCISE:
Create (fake!) a table of ``measured values with errors'' according to
|
(3.2) |
with coming from a Gauss distribution with suitable variance, and
with the function defined by
|
(3.3) |
(
being a set of arbitrary coefficients).
Using these data, try to reconstruct the parameters
by fitting the theoretical function to the table points
. The cost function is
|
(3.4) |
Choose an initial vector
and perform an MC random walk
through
-space, slowly lowering the temperature.
Next: 3.4.2 Genetic Algorithms
Up: 3.4 Stochastic Optimization
Previous: 3.4 Stochastic Optimization
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001