in reply to Re^10: Tricky chemicals optimization problem
in thread Tricky chemicals optimization problem

Thanks again for the thoughtful replies, I'm learning a bunch each iteration here (hope it's not irritating for you).

In response to your call outs : I don't understand how you can "minimixe the number of nozzles"? Don't you need all the different flows to be separate? If not, why are there multiple flows of the same chemical on the same machine in the existing scheme? So if a chemical is the same, and its nozzle is on the same machine it can be collapsed into one. The reason my data is showing differently is because it represents real world inefficiencies in the manufacturing. Essentially the case you pointed out is an easy win or is a particular exception (perhaps due to flow rate which we don't know ). We are assuming now that it's always the former case, to simplify the analysis.

 If you don't care how many machines, just have a separate machine for each chemical; and if the total flow required for a given chemical exceeds the machines capacity, add another for that chemical.

I explained this poorly. What I should.have said is : we want to minimize the numbers of nozzles with precedence over minimizing the number of machines. The relative weighting of each is something I'm been thinking a lot about, but st a high level the minimizing of nozzles has to take precedence over minimizing of machines, that being said you still want to end with the fewest machines possible.

The code I supplied does a pretty good job of putting as many of the flows for a given chemical onto the same machine. If you can combine flows to a single nozzle, simply adding all the flows for a given chemical on a given machine into single nozzle will do a pretty good job of minimizing the number of nozzles.

I hear what you are saying but I'm failing to see what the gap might be if we made minimizing the lines higher precedence... I.e., is the fact that your code is doing a good job of minimizing the nozzles a side effect of the operation , or are you purposefully designing it to do that -if so can you point out the line that provides that effect? If you switch all like chemical nozzles across different machines e.g., let's say : Mach A Chem A 45%, Mach B Chem A 30%, Mach C Chem A 40% , where the percents represent the percent of total capacity that flow value would take of a single machines capacity, the result you'd want is Mach A Chem A 85% (A+ C ), and then a second machine Mach B remains at 30% for Chem A because Mach A does not have the capacity left to take on this 30% block. Once you do this you would search for the optimal solution to fill in the remaining 15% capacity in Mach A with a different chemical(s), and 70% on Mach B with different chemical(s). Ideal here would be a second chemical that runs 10% on 7 machines, and thus can be collapsed into one nozzle that perfectly utilizes the 70% capacity remaining on machine B. Does the greedy algorithm approach still work optimally here? Or maybe a gradient descent? I'm really struggling to program in the logic I just described via the Chem A ,Chem B example due to the large numbers of machines and chemicals

The code I posted already puts all the flows for a given chemical on a given machine into a separate array, so combining them would be trivial, assuming that there in no limit on the flow from a nozzle other than the machine limit. (A question I did ask but you didn't answer as far as I've noticed.) Which array is this in the code you provided?

Re: flow - the 'flow' values (3rd column of the data) are actually seconds of flow, and the machines total capacity is also represented as seconds of flow. You must think of them as blocks though, as you currently are I.e., you can sum the seconds 'blocks' but not not split them into pieces.

On books- I definitely will do that and start reading this weekend. Thanks a ton for the help again. You're a wizard with this stuff.

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Re^12: Tricky chemicals optimization problem
by BrowserUk (Patriarch) on Jan 11, 2017 at 23:02 UTC

    I can answer these two questions tonight, the others will have to wait until Friday.

    Which array is this in the code you provided?

    If you look at the second block of output (100,000 nearest to your 85,000 machine limit) in Re^6: Tricky chemicals optimization problem, and I reformat the first line for machine E001 thus:

    E001 => { 
    " total" => 99982.9104, 
    C015 => [24504.1632, 14837.91, 13323.6396, 12250.6656, 6234.5772, 
+5720.64, 5255.838, 4380.3252, 3468.138, 2386.0308, 1716.192, 1501.668
+, 1436.2488, 1430.16, 791.19, 703.4688],
    C064 => [42.0552] 
},

    [download]

    You can see that although the machine has 17 flows from the original dataset, they are made up of just two chemicals. So, by your latest description, that machine only requires two nozzles.

    I hear what you are saying but I'm failing to see what the gap might be if we made minimizing the lines higher precedence... I.e., is the fact that your code is doing a good job of minimizing the nozzles a side effect of the operation , or are you purposefully designing it to do that -if so can you point out the line that provides that effect?

    The fact that the loops of code attempt to fill each machine from flows of Cnnn first (largest first due to the sorting), and only switches to other chemicals when there are either no flows for this chemical left; or there are no flows of the current chemical that will fit in the remaining space, means that the very act of attempting to use the minimal number of machines will also ensure that each chemical is spread to as few machines as possible (within the limitations of the greedy algorithm).

    The upshot of that is that is all the flows of particular chemical on any given machine can be combined into one nozzle; and thus minimizing the number of machines also tends to minimize the number of nozzles. (Again, within the limitations of the greedy algorithm.

    Those greedy algorithm limitations mean that it may be possible to reduce the nozzle count a little by juggling the smaller components around; but it will only be a very small percentage.

    If that was actually necessary; then you move into the realms of either:

    • Genetic programming:

      Try swapping a few things around in a few random combinations and then discard the some of the least good ones. Rinse and repeat until either no further improvement has been seen for some number of iterations; or until some time limit is reached.

    • A full brute force, exhaustive search.

      This method is guaranteed to find the absolute optimum solution. Eventually! But even for the relatively small number of thing you are dealing with, it is apt to take many days or even weeks to run.

    With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
    Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
    "Science is about questioning the status quo. Questioning authority". The enemy of (IT) success is complexity.
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      Hey UK, Is there any chance you can suggest which parts of the code I need to focus on to accomplish the change to minimizing nozzles before minimizing number of machines? Even if it's simpler to minimize nozzles and not worry about machines I can probably take it further from that point - I'm a bit stuck at the moment

      thanks again for the help /thoughts
[reply]
        which parts of the code I need to focus on to accomplish the change to minimizing nozzles before minimizing number of machines?

        Well, the minimum number of nozzles is simply the number of chemicals; plus that number required to ensure that no single nozzle is delivering more than your machine limit.

        This code, simply reads your sample data, discards any 'zero flows' and accumulates all flows for each chemical.

        <Reveal this spoiler or all spoilers in this node or all in this thread>
        The provisional result is that there are 406 non-zero flows for 61 chemicals. But, some of those chemicals have combined flows that are greater than the 85,000 seconds/machine you've stipulated. Those need to be split across 2 or more machines. Doing so results in a requirement for 71 machines to dispense the 61 chemicals:
        <Reveal this spoiler>

        But now, some of the machines (eg.those running C057 & C039) are grossly under-utilised and those chemicals need to be combined into fewer machines.

        The simplest approach to that is a variation of the greedy knapsack algorithm which I will call (because I haven't seen it described anywhere) and the max-min algorithm.

        Basically you order the nozzles largest to smallest. You look at the largest and then track backward from the smallest until you find the largest (single chemical) nozzle that can be combined with that largest nozzle without breaking the machine limit. Combine them into a single machine and remove the small one from them from consideration. Rinse and repeat. When the smallest left is too big to be combined, remove the current largest from consideration also. Rinse and repeat until no nozzles are left.

        This isn't guaranteed to produce the absolute optimal solution in terms of minimizing the number of machines, but it will always produce the minimum number of nozzles and very close to the minimal number of machines.

        I don't have code for this approach this evening, but I'll try to post some tomorrow.

        With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority". The enemy of (IT) success is complexity.
        In the absence of evidence, opinion is indistinguishable from prejudice.
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