Constrined dependent optimization.

Thank you for the suggestion but I am not sure how to formulate the
problem in linear programming terms. Stated very simply the problem
is a warehouse problem. We are trying to place the items in an
optimal position so as to minimize the distance needed to travel to
pick the items to fulfill an order. For example an order would come
in for A, B, C. In the worst case A would be on one end of the
warehouse, B in the middle and C on the other end. The ideal case
would be that A, B, and C are within close proximity. So the
variables are the positions of the items in the warehouse. The
distance function would be the distance from A to B plus the distance
from B to C (assuming the absolute locations are sorted). The
function that I would like to minimize would be average distance for
all orders over say the last month. So the large number of variables
is due to the large number of items and positions in the warehouse.
So having explained myself a little better does it still sound to you
like a linear programming problem? I am having a hard time thinking
of it in those terms.

Thanks again.

Kevin

---- Ben Bolker <bolker at ufl.edu> wrote:

rkevinburton wrote:

Thank you I had not considered using "gradient" in this fashion.
Now as an add on question. You (an others) have suggested using
SANN. Does your answer change if instead of 100 "variables" or
bins there are 20,000? From the documentation L-BFGS-B is
designed for a large number of variables. But maybe SANN can
handle this as well.

Kevin

It's a question of time and space.  Try the problem for 100, 500,
1000 ... variables to see how the memory usage and time scale.  (At
a guess, memory will be linear in N and not too bad, time will be
horrible.) I haven't followed the thread very carefully, if any of
the linear programming solutions solve your problem they will be
far more efficient. It sounds as  though you have an extremely
non-trivial optimization problem here, the brute-force approach
exemplified by SANN may not work, so you will have to map your
problem onto a framework (such as linear programming) that strives
for efficiency rather than generality. (L-BFGS-B is out of the
question.)

Essentially, this is turning into an optimization problem rather
than an R problem. Once you know that there exists an optimization
approach that can solve your problem before the sun burns out, you
can come back and find out if anyone has implemented it in R (or
RSiteSearch() for it ...), or implemented an interface with a
lower-level platform.

Good luck, Ben Bolker -- View this message in context:
http://www.nabble.com/Constrined-dependent-optimization.-tp22772520p22834746.html
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