Integer Programming in Python
An Integer Programming problem is a problem constructed to ensure mathematical optimization or feasibility by providing that some or all of the variables involved in the issue are integers.
Suppose some decision variables in the problem are found not to be discrete. In that case, they are classified as a mixedinteger problem, more commonly known as MIP/MILP
(MixedInteger Linear Programming).
So in this Python article, we will explore the various methodologies and libraries we can use to solve these kinds of problems in Python.
MixedInteger Programming Problems in Python
A mixedinteger programming (MIP
) problem is a problem in which some decision variables are ensured to be strictly integer values for an optimal solution.
Using these integer variables broadens the horizon and score of helpful optimization problems that a programmer can use to define and solve most efficiently and accurately.
An essential scenario in MIP
is the decision variable considered binary; in other words, it can only be represented as either 0
or 1
.
These are usually referred to as Binary Integer Values. These decision variables are typically used to model True
/False
or Yes
/No
decisions based on careful calculations.
Now there are several solvers out there that were designed to deal with these kinds of problems.
These include the stateoftheart Gurobi
and PythonMIP
, among the most commonly known and soughtafter mixedinteger linear programming solvers.
Another highly configurable MIP
solver is the CBC
or COINOR Branch&Cut
solver. Finally, PythonMIP
makes developing highperforming, MIPbased solvers for any custom application easy.
It provides highend and modern features, described and explained in full detail below.
Python Tools for MIP/MILP
: PythonMIP
In Python, we have a vast library called MIP
, essentially a collection of Pythonbased tools for modelling and solving mixedinteger linear programming problems.
With a syntax inspired greatly by Pulp
, MIP
provides the users access to advanced and efficient features like lazy constraints
, MIPstart
, solution pools
, and cut generation
.
More of its prominent features include:

Highlevel Modeling
Most programmers have developed their skills in modelling using a highlevel programming language as it is easy. However, we can write our
MIP models
in Python quickly.The operator overloading feature makes the whole process of writing linear expressions much smoother in Python.

Feature Packed
With features like
cut generators
andlazy constraints
, a programmer can work with solid formulations using many constraints.It generates only the inequalities required during the
branch and cut
search. Then, to add, you can query into thesolution pool
to extract or go through the topnotch solutions found during the search.Furthermore,
MIPstart
enables a programmer to initially utilize a problemdependent heuristic to create feasible solutions for theMIP
search. 
Fast & Efficient
The
MIP
package in Python makes a directcall
to the native dynamic loadable library of the already installed solver using theCFFI module
.These models are efficiently stored and made efficient by the solver. Meanwhile,
MIP
deals with communicating with your code. While the officialGurobi
Python interface also provides features to handleMILP
, theMIP
library in Python is compatible withPypy
.It can run
25
times faster than it, as its performance is based onCPython
only. 
Multisolve
MIP
in Python was constructed to be thoroughly integrated with theCbased libraries
of theCOINOR Branch&Cut
solver andGurobi
.With
MIP
, you don’t have to worry about writing a means for communication between different solvers, as it is dealt with in thePythonMIP
library.You need only write a single, solverindependent code.

Equipped with the Latest Python Versions
As mentioned above,
MIP
is compatible with Python versions 3.6 and above, so we don’t have to worry about redundancy slowing you down.
Now you know what mixedInteger Programming is and the different solvers available to guide you through any integer programming problem that may need solving in the most efficient and usefully optimized manner.
You can also explore the official documentation for all the solvers mentioned to find solutions for your specific problem.
My name is Abid Ullah, and I am a software engineer. I love writing articles on programming, and my favorite topics are Python, PHP, JavaScript, and Linux. I tend to provide solutions to people in programming problems through my articles. I believe that I can bring a lot to you with my skills, experience, and qualification in technical writing.
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