Abstract problem, any known solutions?

Folks, This is an abstract of a real life engineering problem that I'm
working on, not homework. I've managed to implement a partially effective
algorithm, but the code is clunky, and just wonder whether there's a
standard, elegant solution out there. My solutions are presently based on
(a) filling in the biggest gaps from the centre first and (b) minimising a
hypothetical 'unbalance moment'.
A cylindrical central feed distributor, with 'n' processing units being fed
through radial, evenly spaced feed lines. Each line has an on/off valve, ie.
each unit may be off or on, no in-between. The number of online units is
being adjusted by a separate controller, in response to production
requirements.
The algo needs to choose units to switch to maximise the flow symmetry in
the central distributor, eg. 1/3/5/7 is good, 1/2/3 is bad.
Any suggestions appreciated.
Reply to
Bruce Varley
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I don't think I have enough information to go on (mostly it's not clear what's being distributed (liquid? powder? pellets?), how quickly and easily it can flow around your cylindrical distributor (which I assume is really an annulus), what the cost is if you don't have good distribution (presumably product on the floor, a big mess, and lost raw materials -- but how soon does this happen compared to when your downstream operations run out of material?).
But if it's any consolation, from the way you frame the problem I don't know that I could do anything that's not clunky.
Do you have a good vision of how to do it manually?
Reply to
Tim Wescott
Thanks Tim. That overcomplicates the problem somewhat, it's just about achieving mathematical symmetry around the circle. I've already done a reasonable job with scrappy code as I mentioned. There are some extensions if you can make a prediction of future states, for example, in the 8-case, if you have 1,5 and add one, minimum imbalance (as in moments) is achieved by adding, eg. 2, but if you know that you're going to add another one shortly, 3 would be better (followed by 7). That would make my code even more messy, I just wondered whether anyone somewhere has a 'book proof'. I know it's a long shot.

Reply to
Bruce Varley
I guess I'm just not visualizing what you're trying to do, and thus can't quite figure out what you need. The reason I was asking about material is because if you're dumping in some viscous fluid, you could in theory service the #4 outlet with the #1 inlet, just with a rate limitation. But if you're dumping in sand, then you can't, period.
Without knowing the in/out relationship, I think there's not algorithm to be had. And I don't see how to see the in/out relationship without knowing the material characteristics.
But -- clunky but working is a lot better than an elegant failure!
Reply to
Tim Wescott

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