[SciPy-Dev] optimize: add algorithm for global optimization basin hopping

josef.pktd@gmai... josef.pktd@gmai...
Wed Oct 10 14:24:21 CDT 2012

On Wed, Oct 10, 2012 at 2:55 PM, Ralf Gommers <ralf.gommers@gmail.com> wrote:
> On Tue, Oct 9, 2012 at 11:30 PM, Jacob Stevenson <jstevenson131@gmail.com>
> wrote:
>> Hi everyone, I just submitted a pull request to incorporate a basinhopping
>> routine in the optimize package.  Basinhopping is a powerful algorithm, but
>> all the hard work would be done by the minimizers that already exist in
>> scipy.optimize, so the additional code needed is really not very much.
>> The following is from the documentation notes:
>> Basin hopping is a random algorithm which attempts to find the global
>> minimum of a smooth scalar function of one or more variables.  The algorithm
>> was originally described by David Wales http://www-wales.ch.cam.ac.uk/ .
>> The algorithm is iterative with each iteration composed of the following
>> steps
>> 1) random displacement of the coordinates
>> 2) local minimization
>> 3) accept or reject the new coordinates based on the minimized function
>> value.
>> This global minimization method has been shown to be extremely efficient
>> on a wide variety of problems in physics and chemistry.  It is especially
>> efficient when the function has many minima separated by large barriers.
>> See the Cambridge Cluster Database http://www-wales.ch.cam.ac.uk/CCD.html
>> for database of molecular systems that have been optimized primarily using
>> basin hopping.  This database includes minimization problems exceeding 300
>> degrees of freedom.
>> Thanks,
>> Jake
>> p.s. this is my first post and first submission
> Hi Jake, welcome!
> It looks to me like basin hopping would be a nice addition to
> scipy.optimize. It looks quite similar to simulated annealing, which we
> already have, and may be more efficient for certain classes of problems.
> You're hinting at that already in the notes section, but more details on
> that comparison would be good to put in the docs. A benchmark comparing your
> algorithm with anneal() would be good to see also.

A comparison would be useful, but I think the differences are large
enough that the relative benefits would depend a lot on the problem.

Anneal has to many tuning parameters, and like most of these global
optimizers they use a large number of function evaluations even close
to the optimum. (my impression)

My impression is that hybrid optimizers, like basinhopping, are much
better for problems that have several local minima but still have a
nice local behavior. Several of the problems in statsmodels would fall
into this category.

I sent a while ago a message to the user mailing list ("OT: global
optimizati​on, hybrid global local search").

I think this kind of optimizers would be a good addition to scipy, and
I would be glad to be able to use something more systematic than just
picking several random starting values for local optimization.

<a user>

> This PR made me wonder what other algorithms would be good to have, and
> what's out of scope for scipy. My feeling is that some similar stochastic
> algorithms to this one could be nice to have, but that other types of global
> optimizers are out of scope - there's OpenOpt, IPOPT, PyGMO, PyEvolve etc.
> for that.
> Cheers,
> Ralf
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