---
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PySwarms is an extensible research toolkit for particle swarm optimization
(PSO) in Python.
It is intended for swarm intelligence researchers, practitioners, and
students who prefer a high-level declarative interface for implementing PSO
in their problems. PySwarms enables basic optimization with PSO and
interaction with swarm optimizations. Check out more features below!
* **Free software:** MIT license
* **Documentation:** https://pyswarms.readthedocs.io.
* **Python versions:** 3.5 and above
## Features
* High-level module for Particle Swarm Optimization. For a list of all optimizers, check [this link].
* Built-in objective functions to test optimization algorithms.
* Plotting environment for cost histories and particle movement.
* Hyperparameter search tools to optimize swarm behaviour.
* (For Devs and Researchers): Highly-extensible API for implementing your own techniques.
[this link]: https://pyswarms.readthedocs.io/en/latest/features.html
## Installation
To install PySwarms, run this command in your terminal:
```shell
$ pip install pyswarms
```
This is the preferred method to install PySwarms, as it will always install
the most recent stable release.
In case you want to install the bleeding-edge version, clone this repo:
```shell
$ git clone -b development https://github.com/ljvmiranda921/pyswarms.git
```
and then run
```shell
$ cd pyswarms
$ python setup.py install
```
## Running in a Vagrant Box
To run PySwarms in a Vagrant Box, install Vagrant by going to
https://www.vagrantup.com/downloads.html and downloading the proper packaged from the Hashicorp website.
Afterward, run the following command in the project directory:
```shell
$ vagrant provision
$ vagrant up
$ vagrant ssh
```
Now you're ready to develop your contributions in a premade virtual environment.
## Basic Usage
PySwarms provides a high-level implementation of various particle swarm
optimization algorithms. Thus, it aims to be user-friendly and customizable.
In addition, supporting modules can be used to help you in your optimization
problem.
### Optimizing a sphere function
You can import PySwarms as any other Python module,
```python
import pyswarms as ps
```
Suppose we want to find the minima of `f(x) = x^2` using global best
PSO, simply import the built-in sphere function,
`pyswarms.utils.functions.sphere()`, and the necessary optimizer:
```python
import pyswarms as ps
from pyswarms.utils.functions import single_obj as fx
# Set-up hyperparameters
options = {'c1': 0.5, 'c2': 0.3, 'w':0.9}
# Call instance of PSO
optimizer = ps.single.GlobalBestPSO(n_particles=10, dimensions=2, options=options)
# Perform optimization
best_cost, best_pos = optimizer.optimize(fx.sphere, iters=100)
```
This will run the optimizer for `100` iterations, then returns the best cost
and best position found by the swarm. In addition, you can also access
various histories by calling on properties of the class:
```python
# Obtain the cost history
optimizer.cost_history
# Obtain the position history
optimizer.pos_history
# Obtain the velocity history
optimizer.velocity_history
```
At the same time, you can also obtain the mean personal best and mean neighbor
history for local best PSO implementations. Simply call `optimizer.mean_pbest_history`
and `optimizer.mean_neighbor_history` respectively.
### Hyperparameter search tools
PySwarms implements a grid search and random search technique to find the
best parameters for your optimizer. Setting them up is easy. In this example,
let's try using `pyswarms.utils.search.RandomSearch` to find the optimal
parameters for `LocalBestPSO` optimizer.
Here, we input a range, enclosed in tuples, to define the space in which the
parameters will be found. Thus, `(1,5)` pertains to a range from 1 to 5.
```python
import numpy as np
import pyswarms as ps
from pyswarms.utils.search import RandomSearch
from pyswarms.utils.functions import single_obj as fx
# Set-up choices for the parameters
options = {
'c1': (1,5),
'c2': (6,10),
'w': (2,5),
'k': (11, 15),
'p': 1
}
# Create a RandomSearch object
# n_selection_iters is the number of iterations to run the searcher
# iters is the number of iterations to run the optimizer
g = RandomSearch(ps.single.LocalBestPSO, n_particles=40,
dimensions=20, options=options, objective_func=fx.sphere,
iters=10, n_selection_iters=100)
best_score, best_options = g.search()
```
This then returns the best score found during optimization, and the
hyperparameter options that enable it.
```s
>>> best_score
1.41978545901
>>> best_options['c1']
1.543556887693
>>> best_options['c2']
9.504769054771
```
### Swarm visualization
It is also possible to plot optimizer performance for the sake of formatting.
The plotters module is built on top of `matplotlib`, making it
highly-customizable.
```python
import pyswarms as ps
from pyswarms.utils.functions import single_obj as fx
from pyswarms.utils.plotters import plot_cost_history, plot_contour, plot_surface
import matplotlib.pyplot as plt
# Set-up optimizer
options = {'c1':0.5, 'c2':0.3, 'w':0.9}
optimizer = ps.single.GlobalBestPSO(n_particles=50, dimensions=2, options=options)
optimizer.optimize(fx.sphere, iters=100)
# Plot the cost
plot_cost_history(optimizer.cost_history)
plt.show()
```
We can also plot the animation...
```python
from pyswarms.utils.plotters.formatters import Mesher, Designer
# Plot the sphere function's mesh for better plots
m = Mesher(func=fx.sphere,
limits=[(-1,1), (-1,1)])
# Adjust figure limits
d = Designer(limits=[(-1,1), (-1,1), (-0.1,1)],
label=['x-axis', 'y-axis', 'z-axis'])
```
In 2D,
```python
plot_contour(pos_history=optimizer.pos_history, mesher=m, designer=d, mark=(0,0))
```
Or in 3D!
```python
pos_history_3d = m.compute_history_3d(optimizer.pos_history) # preprocessing
animation3d = plot_surface(pos_history=pos_history_3d,
mesher=m, designer=d,
mark=(0,0,0))
```
## Contributing
PySwarms is currently maintained by a small yet dedicated team:
- Lester James V. Miranda ([@ljvmiranda921](https://github.com/ljvmiranda921))
- SiobhΓ‘n K. Cronin ([@SioKCronin](https://github.com/SioKCronin))
- Aaron Moser ([@whzup](https://github.com/whzup))
- Steven Beardwell ([@stevenbw](https://github.com/stevenbw))
And we would appreciate it if you can lend a hand with the following:
* Find bugs and fix them
* Update documentation in docstrings
* Implement new optimizers to our collection
* Make utility functions more robust.
We would also like to acknowledge [all our
contributors](http://pyswarms.readthedocs.io/en/latest/authors.html), past and
present, for making this project successful!
If you wish to contribute, check out our [contributing guide].
Moreover, you can also see the list of features that need some help in our
[Issues] page.
[contributing guide]: https://pyswarms.readthedocs.io/en/development/contributing.html
[Issues]: https://github.com/ljvmiranda921/pyswarms/issues
**Most importantly**, first-time contributors are welcome to join! I try my
best to help you get started and enable you to make your first Pull Request!
Let's learn from each other!
## Credits
This project was inspired by the [pyswarm] module that performs PSO with
constrained support. The package was created with [Cookiecutter] and the
[`audreyr/cookiecutter-pypackage`] project template.
[pyswarm]: https://github.com/tisimst/pyswarm
[Cookiecutter]: https://github.com/audreyr/cookiecutter
[`audreyr/cookiecutter-pypackage`]: https://github.com/audreyr/cookiecutter-pypackage
## Cite us
Are you using PySwarms in your project or research? Please cite us!
* Miranda L.J., (2018). PySwarms: a research toolkit for Particle Swarm Optimization in Python. *Journal of Open Source Software*, 3(21), 433, [https://doi.org/10.21105/joss.00433](https://doi.org/10.21105/joss.00433)
```bibtex
@article{pyswarmsJOSS2018,
author = {Lester James V. Miranda},
title = "{P}y{S}warms, a research-toolkit for {P}article {S}warm {O}ptimization in {P}ython",
journal = {Journal of Open Source Software},
year = {2018},
volume = {3},
issue = {21},
doi = {10.21105/joss.00433},
url = {https://doi.org/10.21105/joss.00433}
}
```
### Projects citing PySwarms
Not on the list? Ping us in the Issue Tracker!
* Gousios, Georgios. Lecture notes for the TU Delft TI3110TU course Algorithms and Data Structures. Accessed May 22, 2018. http://gousios.org/courses/algo-ds/book/string-distance.html#sop-example-using-pyswarms.
* Nandy, Abhishek, and Manisha Biswas., "Applying Python to Reinforcement Learning." *Reinforcement Learning*. Apress, Berkeley, CA, 2018. 89-128.
* Benedetti, Marcello, et al., "A generative modeling approach for benchmarking and training shallow quantum circuits." *arXiv preprint arXiv:1801.07686* (2018).
* VrbanΔiΔ et al., "NiaPy: Python microframework for building nature-inspired algorithms." Journal of Open Source Software, 3(23), 613, https://doi.org/10.21105/joss.00613
* HaΜse, Florian, et al. "Phoenics: A Bayesian optimizer for chemistry." *ACS Central Science.* 4.9 (2018): 1134-1145.
* Szynkiewicz, Pawel. "A Comparative Study of PSO and CMA-ES Algorithms on Black-box Optimization Benchmarks." *Journal of Telecommunications and Information Technology* 4 (2018): 5.
* Mistry, Miten, et al. "Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded." Imperial College London (2018).
* Vishwakarma, Gaurav. *Machine Learning Model Selection for Predicting Properties of High Refractive Index Polymers* Dissertation. State University of New York at Buffalo, 2018.
* Uluturk Ismail, et al. "Efficient 3D Placement of Access Points in an Aerial Wireless Network." *2019 16th IEEE Anual Consumer Communications and Networking Conference (CCNC)* IEEE (2019): 1-7.
* Downey A., Theisen C., et al. "Cam-based passive variable friction device for structural control." *Engineering Structures* Elsevier (2019): 430-439.
* Thaler S., Paehler L., Adams, N.A. "Sparse identification of truncation errors." *Journal of Computational Physics* Elsevier (2019): vol. 397
* Lin, Y.H., He, D., Wang, Y. Lee, L.J. "Last-mile Delivery: Optimal Locker locatuion under Multinomial Logit Choice Model" https://arxiv.org/abs/2002.10153
* Park J., Kim S., Lee, J. "Supplemental Material for Ultimate Light trapping in free-form plasmonic waveguide" KAIST, University of Cambridge, and Cornell University http://www.jlab.or.kr/documents/publications/2019PRApplied_SI.pdf
* Pasha A., Latha P.H., "Bio-inspired dimensionality reduction for Parkinson's Disease Classification," *Health Information Science and Systems*, Springer (2020).
* Carmichael Z., Syed, H., et al. "Analysis of Wide and Deep Echo State Networks for Multiscale Spatiotemporal Time-Series Forecasting," *Proceedings of the 7th Annual Neuro-inspired Computational Elements* ACM (2019), nb. 7: 1-10 https://doi.org/10.1145/3320288.3320303
* Klonowski, J. "Optimizing Message to Virtual Link Assignment in Avionics Full-Duplex Switched Ethernet Networks" Proquest
* Haidar, A., Jan, ZM. "Evolving One-Dimensional Deep Convolutional Neural Netowrk: A Swarm-based Approach," *IEEE Congress on Evolutionary Computation* (2019) https://doi.org/10.1109/CEC.2019.8790036
* Shang, Z. "Performance Evaluation of the Control Plane in OpenFlow Networks," Freie Universitat Berlin (2020)
* Linker, F. "Industrial Benchmark for Fuzzy Particle Swarm Reinforcement Learning," Liezpic University (2020)
* Vetter, A. Yan, C. et al. "Computational rule-based approach for corner correction of non-Manhattan geometries in mask aligner photolithography," Optics (2019). vol. 27, issue 22: 32523-32535 https://doi.org/10.1364/OE.27.032523
* Wang, Q., Megherbi, N., Breckon T.P., "A Reference Architecture for Plausible Thread Image Projection (TIP) Within 3D X-ray Computed Tomography Volumes" https://arxiv.org/abs/2001.05459
* Menke, Tim, Hase, Florian, et al. "Automated discovery of superconducting circuits and its application to 4-local coupler design," arxiv preprint: https://arxiv.org/abs/1912.03322
## Others
Like it? Love it? Leave us a star on [Github] to show your appreciation!
[Github]: https://github.com/ljvmiranda921/pyswarms
## Contributors
Thanks goes to these wonderful people ([emoji key](https://github.com/all-contributors/all-contributors#emoji-key)):
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<table>
<tr>
<td align="center"><a href="https://github.com/whzup"><img src="https://avatars3.githubusercontent.com/u/39431903?v=4" width="100px;" alt=""/><br /><sub><b>Aaron</b></sub></a><br /><a href="#maintenance-whzup" title="Maintenance">π§</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=whzup" title="Code">π»</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=whzup" title="Documentation">π</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=whzup" title="Tests">β οΈ</a> <a href="#ideas-whzup" title="Ideas, Planning, & Feedback">π€</a> <a href="https://github.com/ljvmiranda921/pyswarms/pulls?q=is%3Apr+reviewed-by%3Awhzup" title="Reviewed Pull Requests">π</a></td>
<td align="center"><a href="https://github.com/Carl-K"><img src="https://avatars2.githubusercontent.com/u/13661469?v=4" width="100px;" alt=""/><br /><sub><b>Carl-K</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=Carl-K" title="Code">π»</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=Carl-K" title="Tests">β οΈ</a></td>
<td align="center"><a href="http://www.siobhankcronin.com/"><img src="https://avatars2.githubusercontent.com/u/19956669?v=4" width="100px;" alt=""/><br /><sub><b>SiobhΓ‘n K Cronin</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=SioKCronin" title="Code">π»</a> <a href="#maintenance-SioKCronin" title="Maintenance">π§</a> <a href="#ideas-SioKCronin" title="Ideas, Planning, & Feedback">π€</a></td>
<td align="center"><a href="http://andrewjarcho.com"><img src="https://avatars3.githubusercontent.com/u/1452951?v=4" width="100px;" alt=""/><br /><sub><b>Andrew Jarcho</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=jazcap53" title="Tests">β οΈ</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=jazcap53" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/mamadyonline"><img src="https://avatars1.githubusercontent.com/u/20543370?v=4" width="100px;" alt=""/><br /><sub><b>Mamady</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=mamadyonline" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/jayspeidell"><img src="https://avatars3.githubusercontent.com/u/26357788?v=4" width="100px;" alt=""/><br /><sub><b>Jay Speidell</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=jayspeidell" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/slek120"><img src="https://avatars2.githubusercontent.com/u/3589574?v=4" width="100px;" alt=""/><br /><sub><b>Eric</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Aslek120" title="Bug reports">π</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=slek120" title="Code">π»</a></td>
</tr>
<tr>
<td align="center"><a href="https://github.com/CPapadim"><img src="https://avatars1.githubusercontent.com/u/13984473?v=4" width="100px;" alt=""/><br /><sub><b>CPapadim</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/issues?q=author%3ACPapadim" title="Bug reports">π</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=CPapadim" title="Code">π»</a></td>
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<td align="center"><a href="https://github.com/nik1082"><img src="https://avatars3.githubusercontent.com/u/17260188?v=4" width="100px;" alt=""/><br /><sub><b>Jericho Arcelao</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=nik1082" title="Code">π»</a></td>
<td align="center"><a href="http://www.jdbohrman.xyz"><img src="https://avatars2.githubusercontent.com/u/27848025?v=4" width="100px;" alt=""/><br /><sub><b>James D. Bohrman</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=jdbohrman" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/bradahoward"><img src="https://avatars2.githubusercontent.com/u/24660861?v=4" width="100px;" alt=""/><br /><sub><b>bradahoward</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=bradahoward" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/ThomasCES"><img src="https://avatars2.githubusercontent.com/u/18325841?v=4" width="100px;" alt=""/><br /><sub><b>ThomasCES</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=ThomasCES" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/danielcorreia96"><img src="https://avatars0.githubusercontent.com/u/17486065?v=4" width="100px;" alt=""/><br /><sub><b>Daniel Correia</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Adanielcorreia96" title="Bug reports">π</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=danielcorreia96" title="Code">π»</a></td>
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<td align="center"><a href="https://github.com/fluencer"><img src="https://avatars3.githubusercontent.com/u/6614307?v=4" width="100px;" alt=""/><br /><sub><b>fluencer</b></sub></a><br /><a href="#example-fluencer" title="Examples">π‘</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=fluencer" title="Documentation">π</a></td>
<td align="center"><a href="https://github.com/miguelcocruz"><img src="https://avatars0.githubusercontent.com/u/45034603?v=4" width="100px;" alt=""/><br /><sub><b>miguelcocruz</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=miguelcocruz" title="Documentation">π</a> <a href="#example-miguelcocruz" title="Examples">π‘</a></td>
<td align="center"><a href="https://github.com/stevenbw"><img src="https://avatars1.githubusercontent.com/u/46458390?v=4" width="100px;" alt=""/><br /><sub><b>Steven Beardwell</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=stevenbw" title="Code">π»</a> <a href="#maintenance-stevenbw" title="Maintenance">π§</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=stevenbw" title="Documentation">π</a> <a href="#ideas-stevenbw" title="Ideas, Planning, & Feedback">π€</a></td>
<td align="center"><a href="https://github.com/ndngo"><img src="https://avatars1.githubusercontent.com/u/16291290?v=4" width="100px;" alt=""/><br /><sub><b>Nathaniel Ngo</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=ndngo" title="Documentation">π</a></td>
<td align="center"><a href="https://github.com/Aneal-Sharma"><img src="https://avatars1.githubusercontent.com/u/19873846?v=4" width="100px;" alt=""/><br /><sub><b>Aneal Sharma</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=Aneal-Sharma" title="Documentation">π</a></td>
<td align="center"><a href="https://github.com/citomcclure"><img src="https://avatars2.githubusercontent.com/u/38021988?v=4" width="100px;" alt=""/><br /><sub><b>Chris McClure</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=citomcclure" title="Documentation">π</a> <a href="#example-citomcclure" title="Examples">π‘</a></td>
<td align="center"><a href="http://se4.space/"><img src="https://avatars2.githubusercontent.com/u/42605993?v=4" width="100px;" alt=""/><br /><sub><b>Christopher Angell</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=ctangell" title="Documentation">π</a></td>
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<td align="center"><a href="https://github.com/Kutim"><img src="https://avatars3.githubusercontent.com/u/8309533?v=4" width="100px;" alt=""/><br /><sub><b>Kutim</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/issues?q=author%3AKutim" title="Bug reports">π</a></td>
<td align="center"><a href="https://github.com/ichbinjakes"><img src="https://avatars1.githubusercontent.com/u/20906800?v=4" width="100px;" alt=""/><br /><sub><b>Jake Souter</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Aichbinjakes" title="Bug reports">π</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=ichbinjakes" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/IanBoyanZhang"><img src="https://avatars3.githubusercontent.com/u/4110995?v=4" width="100px;" alt=""/><br /><sub><b>Ian Zhang</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=IanBoyanZhang" title="Documentation">π</a> <a href="#example-IanBoyanZhang" title="Examples">π‘</a></td>
<td align="center"><a href="https://www.zachariahcarmichael.com/"><img src="https://avatars2.githubusercontent.com/u/20629897?v=4" width="100px;" alt=""/><br /><sub><b>Zach</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=craymichael" title="Documentation">π</a></td>
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<tr>
<td align="center"><a href="https://github.com/yasirroni"><img src="https://avatars2.githubusercontent.com/u/48709672?v=4" width="100px;" alt=""/><br /><sub><b>Muhammad Yasirroni</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=yasirroni" title="Documentation">π</a></td>
<td align="center"><a href="https://github.com/ckastner"><img src="https://avatars0.githubusercontent.com/u/15859947?v=4" width="100px;" alt=""/><br /><sub><b>Christian Kastner</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=ckastner" title="Documentation">π</a> <a href="#platform-ckastner" title="Packaging/porting to new platform">π¦</a></td>
<td align="center"><a href="https://github.com/nishnash54"><img src="https://avatars1.githubusercontent.com/u/25393122?v=4" width="100px;" alt=""/><br /><sub><b>Nishant Rodrigues</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=nishnash54" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/msat59"><img src="https://avatars2.githubusercontent.com/u/20813541?v=4" width="100px;" alt=""/><br /><sub><b>msat59</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=msat59" title="Code">π»</a> <a href="https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Amsat59" title="Bug reports">π</a></td>
<td align="center"><a href="https://github.com/diegoroman17"><img src="https://avatars0.githubusercontent.com/u/1294358?v=4" width="100px;" alt=""/><br /><sub><b>Diego</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=diegoroman17" title="Documentation">π</a></td>
<td align="center"><a href="http://www.aquanova-mp.com/"><img src="https://avatars2.githubusercontent.com/u/6449766?v=4" width="100px;" alt=""/><br /><sub><b>Shaad Alaka</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=Archer6621" title="Documentation">π</a></td>
<td align="center"><a href="https://github.com/blazewicz"><img src="https://avatars1.githubusercontent.com/u/13185945?v=4" width="100px;" alt=""/><br /><sub><b>Krzysztof BΕaΕΌewicz</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Ablazewicz" title="Bug reports">π</a></td>
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<tr>
<td align="center"><a href="https://github.com/a310883"><img src="https://avatars2.githubusercontent.com/u/48936633?v=4" width="100px;" alt=""/><br /><sub><b>Jorge Castillo</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=a310883" title="Documentation">π</a></td>
<td align="center"><a href="https://danner-web.de/"><img src="https://avatars3.githubusercontent.com/u/11915163?v=4" width="100px;" alt=""/><br /><sub><b>Philipp Danner</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=dannerph" title="Code">π»</a></td>
<td align="center"><a href="https://github.com/nikhil-sethi"><img src="https://avatars2.githubusercontent.com/u/50928699?v=4" width="100px;" alt=""/><br /><sub><b>Nikhil Sethi</b></sub></a><br /><a href="https://github.com/ljvmiranda921/pyswarms/commits?author=nikhil-sethi" title="Code">π»</a> <a href="https://github.com/ljvmiranda921/pyswarms/commits?author=nikhil-sethi" title="Documentation">π</a></td>
</tr>
</table>
<!-- markdownlint-enable -->
<!-- prettier-ignore-end -->
<!-- ALL-CONTRIBUTORS-LIST:END -->
This project follows the [all-contributors](https://github.com/all-contributors/all-contributors) specification. Contributions of any kind welcome!
Raw data
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"_id": null,
"home_page": "https://github.com/ljvmiranda921/pyswarms",
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"keywords": "pyswarms",
"author": "Lester James V. Miranda",
"author_email": "ljvmiranda@gmail.com",
"download_url": "https://files.pythonhosted.org/packages/ea/c7/2ec3ac6e8e1346d3728379e4845660048e7054e2ddf14c5bdf11f2a8ff7e/pyswarms-1.3.0.tar.gz",
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"description": "\n---\n\n\n[](https://badge.fury.io/py/pyswarms)\n[](https://dev.azure.com/ljvmiranda/ljvmiranda/_build/latest?definitionId=1&branchName=master)\n[](https://pyswarms.readthedocs.io/en/master/?badge=master)\n[](https://raw.githubusercontent.com/ljvmiranda921/pyswarms/master/LICENSE)\n[](https://doi.org/10.21105/joss.00433)\n[](https://github.com/ambv/black)\n[](https://gitter.im/pyswarms/Issues)\n\nPySwarms is an extensible research toolkit for particle swarm optimization\n(PSO) in Python.\n\nIt is intended for swarm intelligence researchers, practitioners, and\nstudents who prefer a high-level declarative interface for implementing PSO\nin their problems. PySwarms enables basic optimization with PSO and\ninteraction with swarm optimizations. Check out more features below!\n\n* **Free software:** MIT license\n* **Documentation:** https://pyswarms.readthedocs.io.\n* **Python versions:** 3.5 and above\n\n## Features\n\n* High-level module for Particle Swarm Optimization. For a list of all optimizers, check [this link].\n* Built-in objective functions to test optimization algorithms.\n* Plotting environment for cost histories and particle movement.\n* Hyperparameter search tools to optimize swarm behaviour.\n* (For Devs and Researchers): Highly-extensible API for implementing your own techniques.\n\n[this link]: https://pyswarms.readthedocs.io/en/latest/features.html\n\n## Installation\n\nTo install PySwarms, run this command in your terminal:\n\n```shell\n$ pip install pyswarms\n```\n\nThis is the preferred method to install PySwarms, as it will always install\nthe most recent stable release.\n\nIn case you want to install the bleeding-edge version, clone this repo:\n\n```shell\n$ git clone -b development https://github.com/ljvmiranda921/pyswarms.git\n```\nand then run\n\n```shell\n$ cd pyswarms\n$ python setup.py install\n```\n\n## Running in a Vagrant Box\n\nTo run PySwarms in a Vagrant Box, install Vagrant by going to \nhttps://www.vagrantup.com/downloads.html and downloading the proper packaged from the Hashicorp website. \n\nAfterward, run the following command in the project directory:\n\n```shell\n$ vagrant provision\n$ vagrant up\n$ vagrant ssh\n```\nNow you're ready to develop your contributions in a premade virtual environment. \n\n## Basic Usage\n\nPySwarms provides a high-level implementation of various particle swarm\noptimization algorithms. Thus, it aims to be user-friendly and customizable.\nIn addition, supporting modules can be used to help you in your optimization\nproblem.\n\n### Optimizing a sphere function\n\nYou can import PySwarms as any other Python module,\n\n```python\nimport pyswarms as ps\n```\n\nSuppose we want to find the minima of `f(x) = x^2` using global best\nPSO, simply import the built-in sphere function,\n`pyswarms.utils.functions.sphere()`, and the necessary optimizer:\n\n```python\nimport pyswarms as ps\nfrom pyswarms.utils.functions import single_obj as fx\n# Set-up hyperparameters\noptions = {'c1': 0.5, 'c2': 0.3, 'w':0.9}\n# Call instance of PSO\noptimizer = ps.single.GlobalBestPSO(n_particles=10, dimensions=2, options=options)\n# Perform optimization\nbest_cost, best_pos = optimizer.optimize(fx.sphere, iters=100)\n```\n\n\n\nThis will run the optimizer for `100` iterations, then returns the best cost\nand best position found by the swarm. In addition, you can also access\nvarious histories by calling on properties of the class:\n\n```python\n# Obtain the cost history\noptimizer.cost_history\n# Obtain the position history\noptimizer.pos_history\n# Obtain the velocity history\noptimizer.velocity_history\n```\n\nAt the same time, you can also obtain the mean personal best and mean neighbor\nhistory for local best PSO implementations. Simply call `optimizer.mean_pbest_history`\nand `optimizer.mean_neighbor_history` respectively.\n\n### Hyperparameter search tools\n\nPySwarms implements a grid search and random search technique to find the\nbest parameters for your optimizer. Setting them up is easy. In this example,\nlet's try using `pyswarms.utils.search.RandomSearch` to find the optimal\nparameters for `LocalBestPSO` optimizer.\n\nHere, we input a range, enclosed in tuples, to define the space in which the\nparameters will be found. Thus, `(1,5)` pertains to a range from 1 to 5.\n\n```python\nimport numpy as np\nimport pyswarms as ps\nfrom pyswarms.utils.search import RandomSearch\nfrom pyswarms.utils.functions import single_obj as fx\n\n# Set-up choices for the parameters\noptions = {\n 'c1': (1,5),\n 'c2': (6,10),\n 'w': (2,5),\n 'k': (11, 15),\n 'p': 1\n}\n\n# Create a RandomSearch object\n# n_selection_iters is the number of iterations to run the searcher\n# iters is the number of iterations to run the optimizer\ng = RandomSearch(ps.single.LocalBestPSO, n_particles=40,\n dimensions=20, options=options, objective_func=fx.sphere,\n iters=10, n_selection_iters=100)\n\nbest_score, best_options = g.search()\n```\n\nThis then returns the best score found during optimization, and the\nhyperparameter options that enable it.\n\n```s\n>>> best_score\n1.41978545901\n>>> best_options['c1']\n1.543556887693\n>>> best_options['c2']\n9.504769054771\n```\n\n### Swarm visualization\n\nIt is also possible to plot optimizer performance for the sake of formatting.\nThe plotters module is built on top of `matplotlib`, making it\nhighly-customizable.\n\n\n```python\nimport pyswarms as ps\nfrom pyswarms.utils.functions import single_obj as fx\nfrom pyswarms.utils.plotters import plot_cost_history, plot_contour, plot_surface\nimport matplotlib.pyplot as plt\n# Set-up optimizer\noptions = {'c1':0.5, 'c2':0.3, 'w':0.9}\noptimizer = ps.single.GlobalBestPSO(n_particles=50, dimensions=2, options=options)\noptimizer.optimize(fx.sphere, iters=100)\n# Plot the cost\nplot_cost_history(optimizer.cost_history)\nplt.show()\n```\n\n\n\nWe can also plot the animation...\n\n```python\nfrom pyswarms.utils.plotters.formatters import Mesher, Designer\n# Plot the sphere function's mesh for better plots\nm = Mesher(func=fx.sphere,\n limits=[(-1,1), (-1,1)])\n# Adjust figure limits\nd = Designer(limits=[(-1,1), (-1,1), (-0.1,1)],\n label=['x-axis', 'y-axis', 'z-axis'])\n```\n\nIn 2D,\n\n```python\nplot_contour(pos_history=optimizer.pos_history, mesher=m, designer=d, mark=(0,0))\n```\n\n\n\nOr in 3D!\n\n```python\npos_history_3d = m.compute_history_3d(optimizer.pos_history) # preprocessing\nanimation3d = plot_surface(pos_history=pos_history_3d,\n mesher=m, designer=d,\n mark=(0,0,0)) \n```\n\n\n\n## Contributing\n\nPySwarms is currently maintained by a small yet dedicated team:\n- Lester James V. Miranda ([@ljvmiranda921](https://github.com/ljvmiranda921))\n- Siobh\u00e1n K. Cronin ([@SioKCronin](https://github.com/SioKCronin))\n- Aaron Moser ([@whzup](https://github.com/whzup))\n- Steven Beardwell ([@stevenbw](https://github.com/stevenbw))\n\nAnd we would appreciate it if you can lend a hand with the following:\n\n* Find bugs and fix them\n* Update documentation in docstrings\n* Implement new optimizers to our collection\n* Make utility functions more robust.\n\nWe would also like to acknowledge [all our\ncontributors](http://pyswarms.readthedocs.io/en/latest/authors.html), past and\npresent, for making this project successful!\n\nIf you wish to contribute, check out our [contributing guide].\nMoreover, you can also see the list of features that need some help in our\n[Issues] page.\n\n[contributing guide]: https://pyswarms.readthedocs.io/en/development/contributing.html\n[Issues]: https://github.com/ljvmiranda921/pyswarms/issues\n\n**Most importantly**, first-time contributors are welcome to join! I try my\nbest to help you get started and enable you to make your first Pull Request!\nLet's learn from each other!\n\n## Credits\n\nThis project was inspired by the [pyswarm] module that performs PSO with\nconstrained support. The package was created with [Cookiecutter] and the\n[`audreyr/cookiecutter-pypackage`] project template.\n\n[pyswarm]: https://github.com/tisimst/pyswarm\n[Cookiecutter]: https://github.com/audreyr/cookiecutter\n[`audreyr/cookiecutter-pypackage`]: https://github.com/audreyr/cookiecutter-pypackage\n\n## Cite us\nAre you using PySwarms in your project or research? Please cite us!\n\n* Miranda L.J., (2018). PySwarms: a research toolkit for Particle Swarm Optimization in Python. *Journal of Open Source Software*, 3(21), 433, [https://doi.org/10.21105/joss.00433](https://doi.org/10.21105/joss.00433)\n\n```bibtex\n@article{pyswarmsJOSS2018,\n author = {Lester James V. Miranda},\n title = \"{P}y{S}warms, a research-toolkit for {P}article {S}warm {O}ptimization in {P}ython\",\n journal = {Journal of Open Source Software},\n year = {2018},\n volume = {3},\n issue = {21},\n doi = {10.21105/joss.00433},\n url = {https://doi.org/10.21105/joss.00433}\n}\n```\n\n### Projects citing PySwarms\nNot on the list? Ping us in the Issue Tracker!\n\n* Gousios, Georgios. Lecture notes for the TU Delft TI3110TU course Algorithms and Data Structures. Accessed May 22, 2018. http://gousios.org/courses/algo-ds/book/string-distance.html#sop-example-using-pyswarms.\n* Nandy, Abhishek, and Manisha Biswas., \"Applying Python to Reinforcement Learning.\" *Reinforcement Learning*. Apress, Berkeley, CA, 2018. 89-128.\n* Benedetti, Marcello, et al., \"A generative modeling approach for benchmarking and training shallow quantum circuits.\" *arXiv preprint arXiv:1801.07686* (2018).\n* Vrban\u010di\u010d et al., \"NiaPy: Python microframework for building nature-inspired algorithms.\" Journal of Open Source Software, 3(23), 613, https://doi.org/10.21105/joss.00613\n* Ha\u0308se, Florian, et al. \"Phoenics: A Bayesian optimizer for chemistry.\" *ACS Central Science.* 4.9 (2018): 1134-1145. \n* Szynkiewicz, Pawel. \"A Comparative Study of PSO and CMA-ES Algorithms on Black-box Optimization Benchmarks.\" *Journal of Telecommunications and Information Technology* 4 (2018): 5.\n* Mistry, Miten, et al. \"Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded.\" Imperial College London (2018).\n* Vishwakarma, Gaurav. *Machine Learning Model Selection for Predicting Properties of High Refractive Index Polymers* Dissertation. State University of New York at Buffalo, 2018.\n* Uluturk Ismail, et al. \"Efficient 3D Placement of Access Points in an Aerial Wireless Network.\" *2019 16th IEEE Anual Consumer Communications and Networking Conference (CCNC)* IEEE (2019): 1-7.\n* Downey A., Theisen C., et al. \"Cam-based passive variable friction device for structural control.\" *Engineering Structures* Elsevier (2019): 430-439.\n* Thaler S., Paehler L., Adams, N.A. \"Sparse identification of truncation errors.\" *Journal of Computational Physics* Elsevier (2019): vol. 397\n* Lin, Y.H., He, D., Wang, Y. Lee, L.J. \"Last-mile Delivery: Optimal Locker locatuion under Multinomial Logit Choice Model\" https://arxiv.org/abs/2002.10153\n* Park J., Kim S., Lee, J. \"Supplemental Material for Ultimate Light trapping in free-form plasmonic waveguide\" KAIST, University of Cambridge, and Cornell University http://www.jlab.or.kr/documents/publications/2019PRApplied_SI.pdf\n* Pasha A., Latha P.H., \"Bio-inspired dimensionality reduction for Parkinson's Disease Classification,\" *Health Information Science and Systems*, Springer (2020).\n* Carmichael Z., Syed, H., et al. \"Analysis of Wide and Deep Echo State Networks for Multiscale Spatiotemporal Time-Series Forecasting,\" *Proceedings of the 7th Annual Neuro-inspired Computational Elements* ACM (2019), nb. 7: 1-10 https://doi.org/10.1145/3320288.3320303\n* Klonowski, J. \"Optimizing Message to Virtual Link Assignment in Avionics Full-Duplex Switched Ethernet Networks\" Proquest\n* Haidar, A., Jan, ZM. \"Evolving One-Dimensional Deep Convolutional Neural Netowrk: A Swarm-based Approach,\" *IEEE Congress on Evolutionary Computation* (2019) https://doi.org/10.1109/CEC.2019.8790036\n* Shang, Z. \"Performance Evaluation of the Control Plane in OpenFlow Networks,\" Freie Universitat Berlin (2020)\n* Linker, F. \"Industrial Benchmark for Fuzzy Particle Swarm Reinforcement Learning,\" Liezpic University (2020)\n* Vetter, A. Yan, C. et al. \"Computational rule-based approach for corner correction of non-Manhattan geometries in mask aligner photolithography,\" Optics (2019). vol. 27, issue 22: 32523-32535 https://doi.org/10.1364/OE.27.032523\n* Wang, Q., Megherbi, N., Breckon T.P., \"A Reference Architecture for Plausible Thread Image Projection (TIP) Within 3D X-ray Computed Tomography Volumes\" https://arxiv.org/abs/2001.05459\n* Menke, Tim, Hase, Florian, et al. \"Automated discovery of superconducting circuits and its application to 4-local coupler design,\" arxiv preprint: https://arxiv.org/abs/1912.03322 \n\n## Others\nLike it? Love it? Leave us a star on [Github] to show your appreciation! \n\n[Github]: https://github.com/ljvmiranda921/pyswarms\n\n## Contributors\n\nThanks goes to these wonderful people ([emoji key](https://github.com/all-contributors/all-contributors#emoji-key)):\n\n<!-- ALL-CONTRIBUTORS-LIST:START - Do not remove or modify this section -->\n<!-- prettier-ignore-start -->\n<!-- markdownlint-disable -->\n<table>\n <tr>\n <td align=\"center\"><a href=\"https://github.com/whzup\"><img src=\"https://avatars3.githubusercontent.com/u/39431903?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Aaron</b></sub></a><br /><a href=\"#maintenance-whzup\" title=\"Maintenance\">\ud83d\udea7</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=whzup\" title=\"Code\">\ud83d\udcbb</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=whzup\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=whzup\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"#ideas-whzup\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/pulls?q=is%3Apr+reviewed-by%3Awhzup\" title=\"Reviewed Pull Requests\">\ud83d\udc40</a></td>\n <td align=\"center\"><a href=\"https://github.com/Carl-K\"><img src=\"https://avatars2.githubusercontent.com/u/13661469?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Carl-K</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=Carl-K\" title=\"Code\">\ud83d\udcbb</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=Carl-K\" title=\"Tests\">\u26a0\ufe0f</a></td>\n <td align=\"center\"><a href=\"http://www.siobhankcronin.com/\"><img src=\"https://avatars2.githubusercontent.com/u/19956669?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Siobh\u00e1n K Cronin</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=SioKCronin\" title=\"Code\">\ud83d\udcbb</a> <a href=\"#maintenance-SioKCronin\" title=\"Maintenance\">\ud83d\udea7</a> <a href=\"#ideas-SioKCronin\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a></td>\n <td align=\"center\"><a href=\"http://andrewjarcho.com\"><img src=\"https://avatars3.githubusercontent.com/u/1452951?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Andrew Jarcho</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=jazcap53\" title=\"Tests\">\u26a0\ufe0f</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=jazcap53\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/mamadyonline\"><img src=\"https://avatars1.githubusercontent.com/u/20543370?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Mamady</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=mamadyonline\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/jayspeidell\"><img src=\"https://avatars3.githubusercontent.com/u/26357788?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Jay Speidell</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=jayspeidell\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/slek120\"><img src=\"https://avatars2.githubusercontent.com/u/3589574?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Eric</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Aslek120\" title=\"Bug reports\">\ud83d\udc1b</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=slek120\" title=\"Code\">\ud83d\udcbb</a></td>\n </tr>\n <tr>\n <td align=\"center\"><a href=\"https://github.com/CPapadim\"><img src=\"https://avatars1.githubusercontent.com/u/13984473?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>CPapadim</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/issues?q=author%3ACPapadim\" title=\"Bug reports\">\ud83d\udc1b</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=CPapadim\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/dfhljf\"><img src=\"https://avatars1.githubusercontent.com/u/7887642?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>JiangHui</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=dfhljf\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/nik1082\"><img src=\"https://avatars3.githubusercontent.com/u/17260188?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Jericho Arcelao</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=nik1082\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"http://www.jdbohrman.xyz\"><img src=\"https://avatars2.githubusercontent.com/u/27848025?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>James D. Bohrman</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=jdbohrman\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/bradahoward\"><img src=\"https://avatars2.githubusercontent.com/u/24660861?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>bradahoward</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=bradahoward\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/ThomasCES\"><img src=\"https://avatars2.githubusercontent.com/u/18325841?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>ThomasCES</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=ThomasCES\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/danielcorreia96\"><img src=\"https://avatars0.githubusercontent.com/u/17486065?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Daniel Correia</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Adanielcorreia96\" title=\"Bug reports\">\ud83d\udc1b</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=danielcorreia96\" title=\"Code\">\ud83d\udcbb</a></td>\n </tr>\n <tr>\n <td align=\"center\"><a href=\"https://github.com/fluencer\"><img src=\"https://avatars3.githubusercontent.com/u/6614307?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>fluencer</b></sub></a><br /><a href=\"#example-fluencer\" title=\"Examples\">\ud83d\udca1</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=fluencer\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"https://github.com/miguelcocruz\"><img src=\"https://avatars0.githubusercontent.com/u/45034603?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>miguelcocruz</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=miguelcocruz\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-miguelcocruz\" title=\"Examples\">\ud83d\udca1</a></td>\n <td align=\"center\"><a href=\"https://github.com/stevenbw\"><img src=\"https://avatars1.githubusercontent.com/u/46458390?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Steven Beardwell</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=stevenbw\" title=\"Code\">\ud83d\udcbb</a> <a href=\"#maintenance-stevenbw\" title=\"Maintenance\">\ud83d\udea7</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=stevenbw\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#ideas-stevenbw\" title=\"Ideas, Planning, & Feedback\">\ud83e\udd14</a></td>\n <td align=\"center\"><a href=\"https://github.com/ndngo\"><img src=\"https://avatars1.githubusercontent.com/u/16291290?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Nathaniel Ngo</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=ndngo\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"https://github.com/Aneal-Sharma\"><img src=\"https://avatars1.githubusercontent.com/u/19873846?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Aneal Sharma</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=Aneal-Sharma\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"https://github.com/citomcclure\"><img src=\"https://avatars2.githubusercontent.com/u/38021988?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Chris McClure</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=citomcclure\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-citomcclure\" title=\"Examples\">\ud83d\udca1</a></td>\n <td align=\"center\"><a href=\"http://se4.space/\"><img src=\"https://avatars2.githubusercontent.com/u/42605993?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Christopher Angell</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=ctangell\" title=\"Documentation\">\ud83d\udcd6</a></td>\n </tr>\n <tr>\n <td align=\"center\"><a href=\"https://github.com/Kutim\"><img src=\"https://avatars3.githubusercontent.com/u/8309533?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Kutim</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/issues?q=author%3AKutim\" title=\"Bug reports\">\ud83d\udc1b</a></td>\n <td align=\"center\"><a href=\"https://github.com/ichbinjakes\"><img src=\"https://avatars1.githubusercontent.com/u/20906800?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Jake Souter</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Aichbinjakes\" title=\"Bug reports\">\ud83d\udc1b</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=ichbinjakes\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/IanBoyanZhang\"><img src=\"https://avatars3.githubusercontent.com/u/4110995?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Ian Zhang</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=IanBoyanZhang\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-IanBoyanZhang\" title=\"Examples\">\ud83d\udca1</a></td>\n <td align=\"center\"><a href=\"https://www.zachariahcarmichael.com/\"><img src=\"https://avatars2.githubusercontent.com/u/20629897?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Zach</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=craymichael\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"https://www.linkedin.com/in/michel-lavoie-71841526/\"><img src=\"https://avatars3.githubusercontent.com/u/3951483?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Michel Lavoie</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Amiek770\" title=\"Bug reports\">\ud83d\udc1b</a></td>\n <td align=\"center\"><a href=\"http://linkedin.com/in/ewelinakaminska/\"><img src=\"https://avatars1.githubusercontent.com/u/42674710?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>ewekam</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=ewekam\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"https://www.linkedin.com/in/ivyna-alves\"><img src=\"https://avatars2.githubusercontent.com/u/18709508?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Ivyna Santino</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=ivynasantino\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#example-ivynasantino\" title=\"Examples\">\ud83d\udca1</a></td>\n </tr>\n <tr>\n <td align=\"center\"><a href=\"https://github.com/yasirroni\"><img src=\"https://avatars2.githubusercontent.com/u/48709672?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Muhammad Yasirroni</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=yasirroni\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"https://github.com/ckastner\"><img src=\"https://avatars0.githubusercontent.com/u/15859947?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Christian Kastner</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=ckastner\" title=\"Documentation\">\ud83d\udcd6</a> <a href=\"#platform-ckastner\" title=\"Packaging/porting to new platform\">\ud83d\udce6</a></td>\n <td align=\"center\"><a href=\"https://github.com/nishnash54\"><img src=\"https://avatars1.githubusercontent.com/u/25393122?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Nishant Rodrigues</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=nishnash54\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/msat59\"><img src=\"https://avatars2.githubusercontent.com/u/20813541?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>msat59</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=msat59\" title=\"Code\">\ud83d\udcbb</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Amsat59\" title=\"Bug reports\">\ud83d\udc1b</a></td>\n <td align=\"center\"><a href=\"https://github.com/diegoroman17\"><img src=\"https://avatars0.githubusercontent.com/u/1294358?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Diego</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=diegoroman17\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"http://www.aquanova-mp.com/\"><img src=\"https://avatars2.githubusercontent.com/u/6449766?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Shaad Alaka</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=Archer6621\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"https://github.com/blazewicz\"><img src=\"https://avatars1.githubusercontent.com/u/13185945?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Krzysztof B\u0142a\u017cewicz</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/issues?q=author%3Ablazewicz\" title=\"Bug reports\">\ud83d\udc1b</a></td>\n </tr>\n <tr>\n <td align=\"center\"><a href=\"https://github.com/a310883\"><img src=\"https://avatars2.githubusercontent.com/u/48936633?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Jorge Castillo</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=a310883\" title=\"Documentation\">\ud83d\udcd6</a></td>\n <td align=\"center\"><a href=\"https://danner-web.de/\"><img src=\"https://avatars3.githubusercontent.com/u/11915163?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Philipp Danner</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=dannerph\" title=\"Code\">\ud83d\udcbb</a></td>\n <td align=\"center\"><a href=\"https://github.com/nikhil-sethi\"><img src=\"https://avatars2.githubusercontent.com/u/50928699?v=4\" width=\"100px;\" alt=\"\"/><br /><sub><b>Nikhil Sethi</b></sub></a><br /><a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=nikhil-sethi\" title=\"Code\">\ud83d\udcbb</a> <a href=\"https://github.com/ljvmiranda921/pyswarms/commits?author=nikhil-sethi\" title=\"Documentation\">\ud83d\udcd6</a></td>\n </tr>\n</table>\n\n<!-- markdownlint-enable -->\n<!-- prettier-ignore-end -->\n<!-- ALL-CONTRIBUTORS-LIST:END -->\n\nThis project follows the [all-contributors](https://github.com/all-contributors/all-contributors) specification. Contributions of any kind welcome!\n\n\n",
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