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.
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On Fri, 29 Apr 2011 15:30:12 +0800, Bruce Varley wrote:

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?
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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.
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On 05/01/2011 12:57 AM, Bruce Varley wrote:

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!
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Tim Wescott
Wescott Design Services
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