pulp

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PuLP is an linear and mixed integer programming modeler written in Python. With PuLP, it is simple to create MILP optimisation problems and solve them with the latest open-source (or proprietary) solvers. PuLP can generate MPS or LP files and call solvers such as GLPK, COIN-OR CLP/CBC, CPLEX, GUROBI, MOSEK, XPRESS, CHOCO, MIPCL, HiGHS, SCIP/FSCIP.

The documentation for PuLP can be found here.

PuLP is part of the COIN-OR project.

Installation

PuLP requires Python 3.7 or newer.

The easiest way to install PuLP is with pip. If pip is available on your system, type:

python -m pip install pulp

Otherwise follow the download instructions on the PyPi page.

Quickstart

Use LpVariable to create new variables. To create a variable x with 0 ≤ x ≤ 3:

from pulp import *
x = LpVariable("x", 0, 3)

To create a binary variable, y, with values either 0 or 1:

y = LpVariable("y", cat="Binary")

Use LpProblem to create new problems. Create a problem called “myProblem” like so:

prob = LpProblem("myProblem", LpMinimize)

Combine variables in order to create expressions and constraints, and then add them to the problem.:

prob += x + y <= 2

An expression is a constraint without a right-hand side (RHS) sense (one of =, <= or >=). If you add an expression to a problem, it will become the objective:

prob += -4*x + y

To solve the problem with the default included solver:

status = prob.solve()

If you want to try another solver to solve the problem:

status = prob.solve(GLPK(msg = 0))

Display the status of the solution:

LpStatus[status]
> 'Optimal'

You can get the value of the variables using value. ex:

value(x)
> 2.0

Essential Classes

  • LpProblem – Container class for a Linear or Integer programming problem

  • LpVariable – Variables that are added into constraints in the LP problem

  • LpConstraint – Constraints of the general form

    a1x1 + a2x2 + … + anxn (<=, =, >=) b

  • LpConstraintVar – A special type of constraint for constructing column of the model in column-wise modelling

Useful Functions

  • value() – Finds the value of a variable or expression

  • lpSum() – Given a list of the form [a1*x1, a2*x2, …, an*xn] will construct a linear expression to be used as a constraint or variable

  • lpDot() – Given two lists of the form [a1, a2, …, an] and [x1, x2, …, xn] will construct a linear expression to be used as a constraint or variable

More Examples

Several tutorial are given in documentation and pure code examples are available in examples/ directory .

The examples use the default solver (CBC). To use other solvers they must be available (installed and accessible). For more information on how to do that, see the guide on configuring solvers.

For Developers

If you want to install the latest version from GitHub you can run:

python -m pip install -U git+https://github.com/coin-or/pulp

On Linux and MacOS systems, you must run the tests to make the default solver executable:

sudo pulptest

Building the documentation

The PuLP documentation is built with Sphinx. We recommended using a virtual environment to build the documentation locally.

To build, run the following in a terminal window, in the PuLP root directory

cd pulp
python -m pip install -r requirements-dev.txt
cd doc
make html

A folder named html will be created inside the build/ directory. The home page for the documentation is doc/build/html/index.html which can be opened in a browser.

Contributing to PuLP

Instructions for making your first contribution to PuLP are given here.

Comments, bug reports, patches and suggestions are very welcome!