starlight wrote:

my algorithms will accept a request for 8 holes but depending on the musical key, and constraints on finger stretch and hole-size it may not find a good solution. I haven't really tried yet.

Some more thoughts on modelling and optimization...

At least one member here has no use for mathematical modelling, believing that physical prototypes are the only way to be sure what is actually going to happen. Another member sees value in mathematical modelling, but has no use for algorithmic optimization, believing that only an experienced flutemaker knows which direction to go to improve a design. I respect both of these people, and see merit in their opinions. Modelling and optimization still have their limitations, and those of us attempting them shouldn't be blind to those limitations.

In particular, what scope do you have for manual adjustments to a printed flute, post-fabrication?

The time taken by global optimization is inherently exponential in the number of dimensions. If you have a good starting point, for fine-tuning an existing design, a good local optimizer can be far more efficient than relying exclusively on a global optimizer. It's nice to have a choice of optimizers, to see which one gives the best results in a reasonable time.

In any case, stick with optimizers that respect bounds or constraints on the geometry, so you don't go chasing after physically impractical designs, like 20 mm finger holes. This is a particular issue if you want to design, say, an 8-hole flute where the bottom two holes are always-open vent holes. The tuning alone doesn't put enough constraints on where to put the vent holes or how big to make them, so you'll probably need to impose artificial constraints on the geometry to make the optimization tractable.