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MathGroup Archive 2004

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Re: parallel NMinimize[]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50567] Re: parallel NMinimize[]
  • From: "Mark Westwood [EPCC]" <markw at epcc.ed.ac.uk>
  • Date: Fri, 10 Sep 2004 04:06:22 -0400 (EDT)
  • Organization: Edinburgh University
  • References: <chmova$a4j$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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
> 


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