linear programming in python?

36
votes

I need to make a linear programming model. Here are the inequalities I'm using (for example):

6x + 4y <= 24
x + 2y <= 6
-x + y <= 1
y <= 2

I need to find the area described by these inequalities, and shade it in a graph, as well as keep track of the vertices of the bounding lines of this area, and draw the bounding line in a different color. See the graph below for an example of what I'm looking for.

image of the points of intersection.

I'm using Python 3.2, numpy, and matplotlib. Are there better modules for linear programming in Python?

7
pythonlinear-programming
Step one convert the system of inequalities into matrix form. - Dan D.
@izomorphius according to wikipedia, linear programming is mathematical optimization: en.wikipedia.org/wiki/Linear_programming - XORcist
@möter agreed -removing my comment. The mistake is mine not the Op's - Ivaylo Strandjev
Your third equation, -x + x <= 1 is a no-op, since it simplifies to 0 <= 1, which is true for all x and y. - Eric
@user24562 Could you please also elaborate the process that you have used for your default code. (using numpy & matplotlib) - Shivam Kotwalia

7 Answers

69
votes

UPDATE: The answer has become somewhat outdated in the past 4 years, here is an update. You have many options:

  • If you do not have to do it Python then it is a lot more easier to do this in a modeling langage, see Any good tools to solve integer programs on linux?

  • I personally use Gurobi these days through its Python API. It is a commercial, closed-source product but free for academic research.

  • With PuLP you can create MPS and LP files and then solve them with GLPK, COIN CLP/CBC, CPLEX, or XPRESS through their command-line interface. This approach has its advantages and disadvantages.

  • The OR-Tools from Google is an open source software suite for optimization, tuned for tackling the world's toughest problems in vehicle routing, flows, integer and linear programming, and constraint programming.

  • Pyomo is a Python-based, open-source optimization modeling language with a diverse set of optimization capabilities.

  • SciPy offers linear programming: scipy.optimize.linprog. (I have never tried this one.)

  • Apparently, CVXOPT offers a Python interface to GLPK, I did not know that. I have been using GLPK for 8 years now and I can highly recommend GLPK. The examples and tutorial of CVXOPT seem really nice!

  • You can find other possibilites at in the Wikibook under GLPK/Python. Note that many of these are not necessarily resticted to GLPK.

20
votes

I'd recommend the package cvxopt for solving convex optimization problems in Python. A short example with Python code for a linear program is in cvxopt's documentation here.

7
votes

The other answers have done a good job providing a list of solvers. However, only PuLP has been mentioned as a Python library to formulating LP models.

Another great option is Pyomo. Like PuLP, you can send the problem to any solver and read the solution back into Python. You can also manipulate solver parameters. A classmate and I compared the performance of PuLP and Pyomo back in 2015 and we found Pyomo could generate .LP files for the same problem several times more quickly than PuLP.

6
votes

The only time a graph is used to solve a linear program is for a homework problem. In all other cases, linear programming problems are solved through matrix linear algebra.

As for Python, while there are some pure-Python libraries, most people use a native library with Python bindings. There is a wide variety of free and commercial libraries for linear programming. For a detailed list, see Linear Programming in Wikipedia or the Linear Programming Software Survey in OR/MS Today.

Disclaimer: I currently work for Gurobi Optimization and formerly worked for ILOG, which provided CPLEX.

4
votes

For solving the linear programming problem, you can use the scipy.optimize.linprog module in SciPy, which uses the Simplex algorithm.

1
votes

I would recommend using the PuLP python package. It has a nice interface and you can use differenty types of algorithms to solve LP.

0
votes

lpsolve is the easiest to me. No need to install separate solver. It comes with in the package.