[r-t] Travelling Salesman Problem

Glenn Taylor gaataylor at blueyonder.co.uk
Thu Jan 25 18:20:47 UTC 2007

You could easily add to your objective function requirements for music
(such as maximising a row count of desired combinations by giving the
nodes values corresponding to the number of musical rows in that lead)

The idea is spot on but I'm not so sure about "easily" - unless you are
planning an exhaustive search - since falseness issues lob a large spanner
into the works. To take a simple illustration:

Suppose lead L1 has musical score 4 whilst leads L2, L3 and L4 each have
musical score 2. It follows that attempting to include L1 would seem to be a
smart move. If, however, L1 is false with each of L2, L3 and L4 then the
inclusion of L1 adds 4 to the overall music score whilst ruling out the
score of 6 that could be contributed in total by L2, L3 and L4. If,
furthermore, the latter three leads are mutually true then the *exclusion*
of L1 is a better move.

I suppose that it might be possible to take this into consideration by
considering a "net musical score" (for want of a better name) for each lead,
but this would be difficult. If L1 is false with lead F1 it may not be the
case that F1 is itself the musical lead, but rather it is the lead that
comes after F1 in its course that is actually the musical one. This is more
of an issue if one is attempting to keep the tenors together.

Dynamic weighting of leads may be necessary (i.e. the weightings change as
the composition develops), but I can't envisage an algorithm that can weight
the "crap now in the hope of rich pickings later" potential of any lead.

Perhaps someone else can?

Glenn Taylor

More information about the ringing-theory mailing list