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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: function with multiple local minima?
Date: Mon, 24 Mar 2008 11:43:01 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"David Doria" <daviddoria@gmail.com> wrote in message 
<fs82n6$44f$1@fred.mathworks.com>...
> Thanks John -
> 
> I've heard of a method called "simulated annealing".  Would
> this help in this case? or would it just get out of the
> small local mins once I am on the correct side - but not
> help get over the "big bump" in the middle?
> 
> Any other thoughts?
> 
> David

There are several tools in the vein of stochastic
optimization - simulated annealing, genetic
algorithms, particle swarm optimizers, and
randomly multiply started optimizers form
the most popular variations.

The idea is to get over the humps using a
probabilistic methodology of some sort. There
is no assurance that you will converge to the
global optimum. No stochastic optimizer can
assure you of this. They can only increase the
probability that you do succeed. 

In the case of stochastic optimizers, think of
them in terms of their physical metaphors.
A genetic algorithm with a larger gene pool
and a long time to converge will be more likely
to give you a good result than the alternative.
Likewise, if you wish to increase the odds of
convergence, a simulated annealing tool with
a slow, long annealing schedule is better than
short and fast. You might even find that a
schedule with "temperature" oscillations, on
a downward trend are useful in the annealing
context. A large particle swarm, covering more
ground, will be more likely to fall into the
basin for the global minimizer than will a
small swarm. And finally, more random starts
will increase the odds of success in a random
multi-start method.

There are also "global" tools out there, though
not in the optimization toolbox. I'd suggest
that they too have their own issues to deal
with.

John