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MathGroup Archive 2004

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Re: parallel NMinimize[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50586] Re: parallel NMinimize[]
  • From: lupos at cheerful.com (robert)
  • Date: Sat, 11 Sep 2004 06:44:39 -0400 (EDT)
  • References: <chmova$a4j$1@smc.vnet.net> <chroam$50c$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Mark Westwood [EPCC]" <markw at epcc.ed.ac.uk> wrote in message news:<chroam$50c$1 at smc.vnet.net>...
> Robert,
> 
> Forgive me if I've misunderstood your problem or differential evolution, 
> but here's a suggestion.
> 
> You want to search for the global minimum of a function on some domain ?
> 
> Define a form of the NMinimize function you wish to evaluate which is 
> parameterised in terms of p, where p = 1, 2, 3, ... is the number of the 
> processor on which the function will run.
> 
> For example, if your whole domain was [0,1) (yes, I know, very simple 
> example, but work with me on this !), if you have P processors and let p 
> be the identifier of the processor, then your function might be:
> 
>   NMinimize[ { f[x], (p-1)/P <= x < (p/P) }, {x}, Method -> 
> "Differential Evolution" ]
> 
> Use the parallel toolkit to send this function to each of the worker 
> processors on your cluster.  Each will then evaluate the function over 
> 1/p of the whole domain.  Bring the answers together and choose the 
> global minimum from them.  You'll have to figure out how each processor 
> knows its own identity yourself, I don't have the parallel toolkit.
> 
> I guess that this approach might break down at the boundaries between 
> sub-domains, so you might want to send overlapping domains out to avoid 
> that problem.
> 
> I don't know what InitialPoints and SearchPoints are, but from the 
> documentation I think that they are:
> 
> InitialPoints - a guess of where to start searching, you would want to 
> ensure that this was within the subdomain passed to each processor.
> 
> SearchPoints - how many points within the domain to examine, more points 
> -> more time, more accuracy and less chance of returning a local minimum.
> 
> Hope this is of some use
> 
> Regards
> Mark Westwood
> Edinburgh Parallel Computing Centre
> 
> robert wrote:
> > dear all,
> > 
> > I am trying to use NMinimize[f[x],x] from a windows based mathematica
> > to minimize the function f[x] which evaluates via RUN[] and rsh remote
> > shell
> > commands on a linux cluster.
> > this works fine so far.
> > 
> > Now I would like to exploit the parallel capabilities of the linux
> > cluster.
> > 
> > usually NMinimize[] calls f[x] for a single value x at one step.
> > the nature of  NMinimize[f[x],x, Method->"DifferentialEvolution"] as I
> > understand it causes a whole population of x values to be evaluated
> > before
> > minimization progresses.
> > In order to profit from the cluster I would need  NMinimize[] to
> > evaluate
> > f[] for the whole populatuion in a single call.
> > e.g. f[{x1,x2,x3,x4,....xn}] with n beeing the size of the actual
> > popolation such that NMinimize[] would call the function to be
> > minimized with a wole list of x values instead of calling it with just
> > a single value. this way the cluster could evaluate all the (time
> > expense) function calls in parallel and return a list of results
> > {f[x1],f[x2],f[x3],    ...  f[xn]} to NMinimize[]
> > 
> > is there any chance to achieve this ?
> > 
> > does anyone know what for the following "DifferentialEvolution"
> > options are used ?
> > 
> > "InitialPoints"  set of initial points
> > "SearchPoints" size of the population used for evolution
> > 
> > note i dont ask for any parallel aktion of mathematica itself.
> > 
> > thanks robert
> >


hi mark, hi michal

thank you for your contributions,
mark, yes this could be a way, ....

but first of all i dont own a parallel grid version of Mathematica.
second its not the NMinimize aktion thats time consuming its the
evaluation of the objective function which is extreme time consuming
consisting on FEM calculations by an linux based FEM package. so the
natural way would be try to calculate the function values parallel on
a linux cluster (which i have access to).

by the time i got some hints from dan lichtblau perhaps its posssible
for me to modify the NMinimize behavier.

regards robert


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