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https://github.com/pypsa/linopy
Linear optimization with N-D labeled arrays in Python
https://github.com/pypsa/linopy
cbc cplex glpk gurobi linear-optimisation linear-optimization optimisation optimization python xarray xpress
Last synced: 26 minutes ago
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Linear optimization with N-D labeled arrays in Python
- Host: GitHub
- URL: https://github.com/pypsa/linopy
- Owner: PyPSA
- License: mit
- Created: 2021-03-22T09:08:29.000Z (almost 4 years ago)
- Default Branch: master
- Last Pushed: 2024-06-10T09:55:30.000Z (8 months ago)
- Last Synced: 2024-06-11T17:32:25.745Z (8 months ago)
- Topics: cbc, cplex, glpk, gurobi, linear-optimisation, linear-optimization, optimisation, optimization, python, xarray, xpress
- Language: Python
- Homepage: https://linopy.readthedocs.io
- Size: 2.84 MB
- Stars: 148
- Watchers: 7
- Forks: 38
- Open Issues: 33
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE.txt
Awesome Lists containing this project
README
# linopy: Optimization with array-like variables and constraints
[](https://pypi.org/project/linopy/)
[](LICENSE.txt)
[](https://github.com/PyPSA/linopy/actions/workflows/test.yml)
[](https://linopy.readthedocs.io/en/latest/)
[](https://codecov.io/gh/PyPSA/linopy)
**L**inear\
**I**nteger\
**N**on-linear\
**O**ptimization in\
**PY**thon
**linopy** is an open-source python package that facilitates **optimization** with **real world data**. It builds a bridge between data analysis packages like [xarray](https://github.com/pydata/xarray) & [pandas](https://pandas.pydata.org/) and problem solvers like [cbc](https://projects.coin-or.org/Cbc), [gurobi](https://www.gurobi.com/) (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.
## Benchmarks
**linopy** is designed to be fast and efficient. The following benchmark compares the performance of **linopy** with the alternative popular optimization packages.
## Main features
**linopy** is heavily based on [xarray](https://github.com/pydata/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](https://dask.org/)
* 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
```bash
pip install linopy
```
or on conda-forge
```bash
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.
```python
>>> 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
```python
>>> 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
```python
>>> 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
```python
>>> 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:
```python
>>> m.solve()
>>> m.objective.value
```
```
17.166
```
... and display the solution as a pandas DataFrame
```python
>>> 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
* [Cbc](https://projects.coin-or.org/Cbc)
* [GLPK](https://www.gnu.org/software/glpk/)
* [HiGHS](https://www.maths.ed.ac.uk/hall/HiGHS/)
* [Gurobi](https://www.gurobi.com/)
* [Xpress](https://www.fico.com/en/products/fico-xpress-solver)
* [Cplex](https://www.ibm.com/de-de/analytics/cplex-optimizer)
* [MOSEK](https://www.mosek.com/)
* [COPT](https://www.shanshu.ai/copt)
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:
- Hofmann, F., (2023). Linopy: Linear optimization with n-dimensional labeled variables.
Journal of Open Source Software, 8(84), 4823, [https://doi.org/10.21105/joss.04823](https://doi.org/10.21105/joss.04823)
A BibTeX entry for LaTeX users is
```latex
@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}
}
```
## License
Copyright 2021 Fabian Hofmann
This package is published under MIT license. See [LICENSE.txt](LICENSE.txt) for details.