# Integer Programming in Python

Abid Ullah Sep 11, 2022

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 mixed-integer problem, more commonly known as `MIP/MILP` (Mixed-Integer 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.

## Mixed-Integer Programming Problems in Python

A mixed-integer 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 state-of-the-art `Gurobi` and `Python-MIP`, among the most commonly known and sought-after mixed-integer linear programming solvers.

Another highly configurable `MIP` solver is the `CBC` or `COIN-OR Branch-&-Cut` solver. Finally, `Python-MIP` makes developing high-performing, MIP-based solvers for any custom application easy.

It provides high-end and modern features, described and explained in full detail below.

### Python Tools for `MIP/MILP`: `Python-MIP`

In Python, we have a vast library called `MIP`, essentially a collection of Python-based tools for modelling and solving mixed-integer 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:

• ##### High-level Modeling

Most programmers have developed their skills in modelling using a high-level 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` and `lazy 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 the `solution pool` to extract or go through the top-notch solutions found during the search.

Furthermore, `MIPstart` enables a programmer to initially utilize a problem-dependent heuristic to create feasible solutions for the `MIP` search.

• ##### Fast & Efficient

The `MIP` package in Python makes a direct `call` to the native dynamic loadable library of the already installed solver using the `CFFI module`.

These models are efficiently stored and made efficient by the solver. Meanwhile, `MIP` deals with communicating with your code. While the official `Gurobi` Python interface also provides features to handle `MILP`, the `MIP` library in Python is compatible with `Pypy`.

It can run `25` times faster than it, as its performance is based on `CPython` only.

• ##### Multi-solve

`MIP` in Python was constructed to be thoroughly integrated with the `C-based libraries` of the `COIN-OR Branch-&-Cut` solver and `Gurobi`.

With `MIP`, you don’t have to worry about writing a means for communication between different solvers, as it is dealt with in the `Python-MIP` library.

You need only write a single, solver-independent 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 mixed-Integer 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.

Author: Abid Ullah

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.