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Ryan D. Alexander wrote:
> 
 Monte-Carlo methods and simulated annealing are good for monomodal
mathematical functions. But is it really the case in MM ? Two ways :
One random based "the genetic algoritms", David E; Goldberg, Addison
Wesley can be benefit because you have not only the "minimum minimorum"
but also the "local minima" of a multimodal function. The most robust
way, a little less expensive, can be the flexible simplex methods
(from G.E.P. Box ? if my memory is right).
Friendly. Yves.
> In attempting to model chromosomes packed within a nucleus, I've decided that I
> need a type of Monte Carlo Minimization routine.  Scouring the Web has turned up
> little in the way progress, so I've turned to you all in NG-Land...
> 
> Essentially I'm looking for an algorithm (in Fortran 77/90, preferably) where I
> may enter a set of initial cartesian coordinates, the associated radii for each
> "chromosome," and an objective function (i.e. Lennard-Jones potential
> function).  Let the program calculate the value of my objective function, Monte
> Carlo (smartly) to re-position the chromosomes, recalculate the potential, etc.,
> etc. until the function value is minimized.
> 
> Anyone's help (books, articles, URL's) would be greatly appreciated!!  If anyone
> in the realm of molecular dynamics, or packing theory (of non-uniform shapes)
> have any ideas, I'd obviously welcome them as well.
> 
> Thanks in advance... (oh & as this is probably not of general interest to these
> ng's please just e-mail me directly if you'd like)
> -- Ryan D. Alexander
> =========================================================
> Ryan D. Alexander, CSU-LBNL NSCORT Ph.D. Trainee
> Colorado State Univ., Dept. of Radiological Health Sciences
> E-mail: ryanalex@lamar.colostate.edu
> Office Ph: 970-491-0520, Dept. Fax: 970-491-0623
> =========================================================

-- 
-------------------------------------------------
I Dr. Yves Boudeville; Theory Group / ENS-Lyon, I
I Institut de Recherches sur la Catalyse, CNRS  I
I 2, Avenue Albert EINSTEIN ;                   I
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I E-mail: boudevil@catalyse.univ-lyon1.fr       I
I http://www.ens-lyon.fr/~boudevil/             I
-------------------------------------------------

Ryan D. Alexander <ryanalex@lamar.colostate.edu> wrote in message
news:3800F279.AD543BD3@lamar.colostate.edu...
> In attempting to model chromosomes packed within a nucleus, I've decided
that I
> need a type of Monte Carlo Minimization routine.  Scouring the Web has
turned up
> little in the way progress, so I've turned to you all in NG-Land...
>

 An interesting alternative to the suggestions already made is the approach
of the algorithm by A.Zilinskas (published as "Optimization of
one-dimensional multimodal functions", Applied Statistics 1978, v27,
p367-375 (Algorithm AS133)). This gives Fortran code, which should also be
available from statlib under directory apstat. This approach seems only
suited to 1-D problems because of the number of function evaluations. It has
the effect of balancing doing extra function evauations in regions where the
function is "roughest", with evaluations in the neighbourhoods of possibly
competing local optima. The locations where the function is evaluated are
decided so as to supply the best improvement of information about the
location of the overall optimum in a statistical sense.

However, the "genetic" algorithms already mentioned seem well suited to the
problem.

http://dasher.wustl.edu/tinker/

--
Jim

Check out my web site  http://www.kressworks.com/
It'll blow your mind (politically), stimulate your senses (artistically)
and provide scientific insights that boggle the mind!

Ryan D. Alexander <ryanalex@lamar.colostate.edu> wrote in message
news:3800F279.AD543BD3@lamar.colostate.edu...
> In attempting to model chromosomes packed within a nucleus, I've decided
that I
> need a type of Monte Carlo Minimization routine.  Scouring the Web has
turned up
> little in the way progress, so I've turned to you all in NG-Land...
>
> Essentially I'm looking for an algorithm (in Fortran 77/90, preferably)
where I
> may enter a set of initial cartesian coordinates, the associated radii for
each
> "chromosome," and an objective function (i.e. Lennard-Jones potential
> function).  Let the program calculate the value of my objective function,
Monte
> Carlo (smartly) to re-position the chromosomes, recalculate the potential,
etc.,
> etc. until the function value is minimized.
>
> Anyone's help (books, articles, URL's) would be greatly appreciated!!  If
anyone
> in the realm of molecular dynamics, or packing theory (of non-uniform
shapes)
> have any ideas, I'd obviously welcome them as well.
>
> Thanks in advance... (oh & as this is probably not of general interest to
these
> ng's please just e-mail me directly if you'd like)
> -- Ryan D. Alexander
> =========================================================
> Ryan D. Alexander, CSU-LBNL NSCORT Ph.D. Trainee
> Colorado State Univ., Dept. of Radiological Health Sciences
> E-mail: ryanalex@lamar.colostate.edu
> Office Ph: 970-491-0520, Dept. Fax: 970-491-0623
> =========================================================
>
>

There was one in SCS "Simulation" like about 1986, but there was a big
debate if the Mt Carlo made a difference. If you bug me a few days
from now, I might dig up a PL/I test program I wrote with the article
refs embedded in it.

Perhaps it can be understood by looking at a related area: In chosing
PDE solution points, Mt Carlo is said to be more effective because
beyond two dimensions, rectangularisation is inefficient. IBM's
million-dollar Simulation Blaster works along those lines by providing
a file of non-random best sampling points so you don't have to use Mt Carlo.


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