[Numpy-discussion] How can I constrain linear_least_squares to integer solutions?

Timothy Hochberg tim.hochberg at ieee.org
Wed Nov 28 12:03:10 EST 2007

On Nov 28, 2007 12:59 AM, Stefan van der Walt <stefan at sun.ac.za> wrote:

> On Tue, Nov 27, 2007 at 11:07:30PM -0700, Charles R Harris wrote:
> > This is not a trivial problem, as you can see by googling mixed integer
> least
> > squares (MILS). Much will depend on the nature of the parameters, the
> number of
> > variables you are using in the fit, and how exact the solution needs to
> be. One
> > approach would be to start by rounding the coefficients that must be
> integer
> > and improve the solution using annealing or genetic algorithms to jig
> the
> > integer coefficients while fitting the remainder in the usual least
> square way,
> > but that wouldn't have the elegance of some of the specific methods used
> for
> > this sort of problem. However, I don't know of a package in scipy that
> > implements those more sophisticated algorithms, perhaps someone else on
> this
> > list who knows more about these things than I can point you in the right
> > direction.
> Would this be a good candidate for a genetic algorithm?  I haven't
> used GA before, so I don't know the typical rate of convergence or its
> applicability to optimization problems.
> Regards
> Stéfan
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If the number of terms is not huge and the function is well behaved; it
might be worth trying the following simple and stupid approach:

   1. Find the floating point minimum.
   2. for each set of possible set of integer coefficients near the FP
      1. Solve for the floating point coefficients with the integer
      coefficients fixed.
      2. If the minimum is the best so far, stash it somewhere for
   3. Return the best set of coefficients.

.  __
.   |-\
.  tim.hochberg at ieee.org
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