[r-t] Method Generator

Don Morrison dfm at ringing.org
Thu Apr 16 22:12:20 UTC 2015

On Thu, Apr 16, 2015 at 5:35 PM, Mark Davies <mark at snowtiger.net> wrote:
> Ah yes, I remember this! Yes, the trouble is every time you relax a
> restriction, even by allowing just one new place notation (such as 78), the
> number of resulting methods increases exponentially.
> However, if you are looking for musical compositions, you are likely to get
> the best results from musical methods with little falseness. You have to be
> a bit careful, because sometimes unexpected method designs can give amazing
> results, but in general if you are going to get lots of run-based music then
> I think you need a method which generates lots of the same type of runs in
> the plain course, in a way such that certain coursing orders are favoured.
> That however is no good if the favoured coursing orders are false against
> each other and so cannot be included in a composition, hence the internal
> falseness shouldn't be too high either.
> It should be possible to use this kind of heuristic to limit the method
> search to a reasonable number of candidate results, even with the place
> notation restrictions completely relaxed. However it would not be completely
> straightforward, give the interaction between the music and the falseness
> and the need to prune section-by-section as the methods are constructed.

Another (at least, I think this is different than what Mark suggested,
though perhaps I've simply misunderstood him), possible way forward
(assuming it is the usual 4 bell runs at one end or the other of the
row that you're seeking) might be to ask "What are the possible place
notations when the treble is in 1-2 and 3-4, combined with the various
possible lead head orders, that allow the generation of the most runs
(albeit not including 1234s or 4321s) at the back?" That's going to be
a noticeably smaller search space. Then take the N winners on that
task, for some N of your choosing, and ask "What methods with these
backworks allow me to get the best overall count?" For each backwork,
that again is more likely to be tractable.

Something like that might be a reasonable heuristic.

Don Morrison <dfm at ringing.org>
"She had heard it said that, before you could understand anybody, you
needed to walk a mile in their shoes, which did not make a whole lot
of sense, because probably after you had walked a mile in their shoes
you  would understand that they were chasing you and accusing you of
the theft of a pair of shoes--although, of course, you could probably
outrun them, owing to their lack of footwear."
             -- Terry Pratchett, _I Shall Wear Midnight_

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