# Playing with Linear Programming on PyPy

Fancy hi-level interfaces often come with a high runtime overhead making them slow. Here is an experiment with building such an interface using constructions that PyPy should be good at optimizing. The idea is to allow the JIT in PyPy to remove the overhead introduced by using a fancy high-level python interface on top of a low-level C interface. The application considered is Linear programming. It is a tool used to solve linear optimization problems. It can for example be used to find the nonnegative values x, y and z that gives the maximum value of

lp = LinearProgram() x, y, z = lp.IntVar(), lp.IntVar(), lp.IntVar() lp.objective = 10*x + 6*y + 4*z lp.add_constraint( x + y + z <= 100 ) lp.add_constraint( 10*x + 4*y + 5*z <= 600 ) lp.add_constraint( 2*x + 2*y + 6*z <= 300 ) lp.add_constraint( x >= 0 ) lp.add_constraint( y >= 0 ) lp.add_constraint( z >= 0 ) maxval = lp.maximize() print maxval print x.value, y.value, z.valueTo benchmark the API I used it to solve a minimum-cost flow problem with 154072 nodes and 390334 arcs. The C library needs 9.43 s to solve this and the pplp interface adds another 5.89 s under PyPy and 28.17 s under CPython. A large amount of time is still spend setting up the problem, but it's a significant improvement over the 20 minutes required on CPython by cvxopt. It is probably not designed to be fast on this kind of benchmark. I have not been able to get cvxopt to work under PyPy. The benchmark used is available here

## Comments

for the first equation do you not perhaps mean f(x,y,z) = 10x+6y+4z instead of z = 10x+6y+4z ?

Yes, there is a typo there, I'll update the post. Thanx for noting.

That seems like a lot of overhead for the wrapper, what is up with that? I mean, I'd expect the wrapper to reasonably quickly pass it off to the C library.

you should try www.solverfoundation.com using ironpython too.

Winston: It is indeed. What cvxopt spends 20 min on I don't know. One guess would be that it is passing the ~2 million coefficients involved to C one by one, possible with a bit of error checking for each of them. As for the 6 s used by pplp, it needs to convert the equations into the matrices glpk wants. That means shuffling the coefficients around a bit and some bookkeeping to keep track of which goes where.

Anonymous: OK, how would the above example look in that case?

Thanx for noting, I've fixed the post (again).

have you tried openopt[1]?

[1] openopt.org

Are you distinguishing between the time it takes to setup the optimization problem and the time it takes to actually solve it?

GLPK is a simplex solver written in C, and CVXOPT is an interior point solver written in Python/C and is not particularly optimized for sparse problem. Nevertheless, you should check the you actually formulate a large sparse problem in CVXOPT, and not a dense one.