Sorry for bombing this list with my MIP problems. Here is another thing,
again in Sage 5.3:
The following (senseless) test code
P = MixedIntegerLinearProgram()
x = P.new_variable(binary=True)
for i in [0..29]:
c = sum(x[j]*(j-i) for j in [0..29])
takes about 1.6 seconds, even though there are only about 900 additions and
multiplications involved. Checking with %prun what goes wrong, I find more
than 50000 copies, deep copies and such which are responsible for this long
running time.
Of course MIP variables are different from polynomial variables, but still
it might be worth to compare with the analogous and hence equally silly
code:
R = PolynomialRing(QQ,"x",30)
for i in [0..29]:
c = sum(R.gen(j)*(j-i) for j in [0..29])
This takes just 0.023 seconds, and no kind of operation is executed more
than 930 times.
Am I doing something wrong, or is the arithmetic with MIP variables
extremely inefficient? I came across this when I found out that the
bottleneck in a big problem was not solving the integer linear program, but
rather creating it!
All the best,
Peter Mueller
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