[FRIAM] Optimization problem

Sat Sep 21 22:59:15 EDT 2019

Gary,

Thanks for posing this problem to the group - it's been fun to have in the
back of the mind for a day. I agree with Pieter that this is a kind of
knapsack problem for which Dynamic Programming is a popular approach where
you would extend to multiple knapsacks.

I might approach it with a variant of the multiple traveling salesman
(mTSP) problem where your purchased tubes are salesman and the tubes you
want cut are cities which all need to be visited once with the constraint
to minimize the number of salesmen and the upper bound on how far each
salesman can travel (6 meters/miles). The difference of the tube cutting
model with mTSP is that the tubes aren't in a spatial layout so you would
use the length of the tube to be cut as the distance to visit that city. I
like that the edges between tubes to be cut that tend to show up in
successful solutions will get reinforced over time. Do you remember Alberto
Gallo's model from Bios where he used ant colony optimization to solve the
problem?

A GA could also be used by indexing the tubes to be cut as genes in the
genome.

Owen has an elegant optimization on the TSP in Agentscript just using
random swaps based on a fitness function - a kind of simulated annealing
heuristic. http://agentscript.org/models/travsalesman.html

Another approach would be a market model where  6m tubes bid on tubes
segments and their value determined by how much a given tube would complete
their unclaimed space. This was similar to Dick Gordon's paint booth
problem at Bios bidding on cars to paint based on the cost of changing
colors.

Stephen

-Stephen

On Fri, Sep 20, 2019, 5:48 PM Steven A Smith <sasmyth at swcp.com> wrote:

> Gary -
>
> I understand better now...
>
> I definitely agree that the *most* naive eyeballing methods can be
> excruciatingly wasteful.
>
> I presume that your conduit length requirements are not precise... that
> you might be designing them to allow for leaving the window partially
> open but otherwise not subject to intrusion or compromise?  That seems
> to complicate the problem but may pose opportunities.  In particular,
> *I* might be looking for solutions which leave me with a *minimum* of
> leftover conduit by making them longer than their shortest possibles in
> some cases.  Or looking at it the other way, even if you don't need to
> leave the windows open much when "locked" a more complete use of the
> material might be obtained by relaxing the length a little without
> compromising security (if a given window can only be opened a few inches
> for example).
>
> I will be interested in hearing the results of whatever optimization (or
> satisficing) method you use yields.
>
> - Steve
>
> PS. regarding guerin's solution, an alternate would be to measure as
> suggested, then cut naively until the remaining spaces are larger than
> the remaining pieces.  Only *then* does one break out the welder and
> begin to piece together as-needed.   I don't think these are equivalent.
>   It also occurs to me that *2* pieces of conduit (end to end, unwelded)
> in a window channel might be *nearly* as effective as a single piece,
> albeit less elegant?
>
> > Hey Steve. The actual project is nothing elaborate. My house has a
> > couple or three dozsen horizontally sliding windows with pretty weak
> > locks. Since I've had a couple of break-ins in the past, I decided
> > that the easiest way to shore up security for that aspect of the house
> > is to just cut short pieces of 3/4 inch conduit to lay horizontally in
> > the spaces where the windows slide. When I want to open a window, I
> > will just stand its conduit piece up, and when I want to "lock" it
> > again, just lay it back horizontally. I asked on FRIAM because instead
> > of just eyeballing it and having lots of extra (even potentially
> > useful in the future) pieces left over, I'd rather use my (and
> > FRIAM's) brain to look at possible ways of optimizing this. Kind of
> > fun actually putting my mind to something for a change (retirement can
> > be boring if you're not careful).
> >
> > On Fri, Sep 20, 2019 at 5:55 PM Steven A Smith <sasmyth at swcp.com> wrote:
> >> Gary -
> >>
> >> I *patently don't* recommend my method, though it does have some
> >> charms.   I recently was faced with a similar problem to yours where I
> >> needed to cut and install trim around the perimeter of the room (with
> >> door openings) I just layed hardwood floor in.
> >>
> >> Rather than go into it in detail (I already did that and realized it was
> >> a TL;DR as usual, so cut it) I will just say that I approach these
> >> problems as *satisficing* and *constraint* problems rather than
> >> *optimization*.    Once I had a candidate layout, I simply looked at the
> >> results and determined that the *waste* was acceptable.   Depending on
> >> the circumstances I sometimes prefer to have for example, 2 3' leftovers
> >> rather than 1 5' leftover, other times, vice-versa, depending on how I
> >> might use said leftovers in some future application (or hedging against
> >> a mistake in my measuring/cutting).
> >>
> >> Care to share what your actual conduit/pipe project is?
> >>
> >> - Steve
> >>
> >>
> >>> Thanks for the links, Peter. I will probably use that software or
> >>> similar, to get a quick solution, then look at the MOOCs.
> >>>
> >>> On Fri, Sep 20, 2019 at 2:52 PM Pieter Steenekamp
> >>> <pieters at randcontrols.co.za> wrote:
> >>>> Two possible approaches are:
> >>>> a) Solve the problem yourself. Use one or a combination of standard
> algorithms ( eg you mentioned linear programming and greedy algorithms,
> there are many more of course) and/or your own custom algorithm. If you
> wish to go this route and want to learn about the subject, I recommend the
> series of MOOCS by Stanford's Tim Roughgarden
> https://www.coursera.org/specializations/algorithms
> >>>> Or, I think yours is probably a knapsack -type problem and the MOOC
> https://www.coursera.org/learn/discrete-optimization covers that
> relatively well.
> >>>> b) But if you just want to get the solution you can use optimization
> software like
> https://www.ibm.com/za-en/products/ilog-cplex-optimization-studio (they
> have a free edition that will be good enough for your application) will
> solve it for you without you necessarily knowing how the software does it.
> >>>>
> >>>> On Fri, 20 Sep 2019 at 21:00, Gary Schiltz <
> gary at naturesvisualarts.com> wrote:
> >>>>> I'd like advice on possible ways to solve the following problem
> >>>>> (plumbers must surely face this all the time). I need to cut a set of
> >>>>> metal tubes of varying lengths from standard length (6 meter)
> >>>>> galvanized conduit stock. The goal is to find the number of tubes I
> >>>>> need to buy, and the order of cuts to produce the minimum amount of
> >>>>> leftover, unused tube.  I'm interested in what types of solutions
> >>>>> people use for similar 1-dimensional problems, e.g. linear
> >>>>> programming, greedy algorithms, etc. (I've been Googling). I'm only
> >>>>> looking to cut around 15-25 pieces, so my gut feeling is that an
> >>>>> exhaustive search of all possible solutions, though probably NP-hard,
> >>>>> would be feasible to perform. Working programs, as well as libraries
> >>>>> in any language would be a bonus.
> >>>>>
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