Linear optimization with N-D labeled arrays in Python

# linopy: Linear optimization with N-dimensional labeled variables

linopy is an open-source python package that facilitates optimization with real world data. It builds a bridge between data analysis packages like xarray & pandas and problem solvers like cbc, gurobi (see the full list below). Linopy supports Linear, Integer, Mixed-Integer and Quadratic Programming while aiming to make linear programming in Python easy, highly-flexible and performant.

## Main features

linopy is heavily based on xarray which allows for many flexible data-handling features:

• Define (arrays of) continuous or binary variables with coordinates, e.g. time, consumers, etc.
• Apply arithmetic operations on the variables like adding, substracting, multiplying with all the broadcasting potentials of xarray
• Apply arithmetic operations on the linear expressions (combination of variables)
• Group terms of a linear expression by coordinates
• Get insight into the clear and transparent data model
• Modify and delete assigned variables and constraints on the fly
• Use lazy operations for large linear programs with dask
• Choose from different commercial and non-commercial solvers
• Fast import and export a linear model using xarray's netcdf IO

## Installation

So far linopy is available on the PyPI repository

pip install linopy


or on conda-forge

conda install -c conda-forge linopy


## In a Nutshell

Linopy aims to make optimization programs transparent and flexible. To illustrate its usage, let's consider a scenario where we aim to minimize the cost of buying apples and bananas over a week, subject to daily and weekly vitamin intake constraints.

>>> import pandas as pd
>>> import linopy

>>> m = linopy.Model()

>>> days = pd.Index(['Mon', 'Tue', 'Wed', 'Thu', 'Fri'], name='day')
>>> apples = m.add_variables(lower=0, name='apples', coords=[days])
>>> bananas = m.add_variables(lower=0, name='bananas', coords=[days])
>>> apples

Variable (day: 5)
-----------------
[Mon]: apples[Mon] ∈ [0, inf]
[Tue]: apples[Tue] ∈ [0, inf]
[Wed]: apples[Wed] ∈ [0, inf]
[Thu]: apples[Thu] ∈ [0, inf]
[Fri]: apples[Fri] ∈ [0, inf]


Add daily vitamin constraints

>>> m.add_constraints(3 * apples + 2 * bananas >= 8, name='daily_vitamins')

Constraint daily_vitamins (day: 5):
-------------------------------------
[Mon]: +3 apples[Mon] + 2 bananas[Mon] ≥ 8
[Tue]: +3 apples[Tue] + 2 bananas[Tue] ≥ 8
[Wed]: +3 apples[Wed] + 2 bananas[Wed] ≥ 8
[Thu]: +3 apples[Thu] + 2 bananas[Thu] ≥ 8
[Fri]: +3 apples[Fri] + 2 bananas[Fri] ≥ 8


Add weekly vitamin constraint

>>> m.add_constraints((3 * apples + 2 * bananas).sum() >= 50, name='weekly_vitamins')

Constraint weekly_vitamins
----------------------------
+3 apples[Mon] + 2 bananas[Mon] + 3 apples[Tue] ... +2 bananas[Thu] + 3 apples[Fri] + 2 bananas[Fri] ≥ 50


Define the prices of apples and bananas and the objective function

>>> apple_price = [1, 1.5, 1, 2, 1]
>>> banana_price = [1, 1, 0.5, 1, 0.5]
>>> m.objective = apple_price * apples + banana_price * bananas


Finally, we can solve the problem and get the optimal solution:

>>> m.solve()
>>> m.objective.value

17.166


... and display the solution as a pandas DataFrame

>>> m.solution.to_pandas()

        apples  bananas
day
Mon    2.667      0
Tue    0          4
Wed    0          9
Thu    0          4
Fri    0          4


## Supported solvers

linopy supports the following solvers

Note that these do have to be installed by the user separately.

## Citing Linopy

If you use Linopy in your research, please cite the following paper:

A BibTeX entry for LaTeX users is

@article{Hofmann2023,
doi = {10.21105/joss.04823},
url = {https://doi.org/10.21105/joss.04823},
year = {2023}, publisher = {The Open Journal},
volume = {8},
number = {84},
pages = {4823},
author = {Fabian Hofmann},
title = {Linopy: Linear optimization with n-dimensional labeled variables},
journal = {Journal of Open Source Software}
}


Copyright 2021 Fabian Hofmann

This package is published under MIT license. See LICENSE.txt for details.

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