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PSOPy

A python implementation of Particle Swarm Optimization.

Introduction

PSOPy (pronounced "Soapy") is a SciPy compatible super fast Python implementation for Particle Swarm Optimization. The codes are tested for standard optimization test functions (both constrained and unconstrained).

The library provides two implementations, one that mimics the interface to scipy.optimize.minimize and one that directly runs PSO. The SciPy compatible function is a wrapper over the direct implementation, and therefore may be slower in execution time, as the constraint and fitness functions are wrapped.

Installation

GitHub

To install this library from GitHub,

$ git clone https://github.com/jerrytheo/psopy.git
$ cd psopy
$ python setup.py install

In order to run the tests,

$ python setup.py test

PyPI

This library is available on the PyPI as psopy. If you have pip installed run,

$ pip install psopy

Examples

Unconstrained Optimization

Consider the problem of minimizing the Rosenbrock function, implemented as scipy.optimize.rosen using a swarm of 1000 particles.

>>> import numpy as np
>>> from psopy import minimize_pso
>>> from scipy.optimize import rosen
>>> x0 = np.random.uniform(0, 2, (1000, 5))
>>> res = minimize_pso(rosen, x0, options={'stable_iter': 50})
>>> res.x
array([1.00000003, 1.00000017, 1.00000034, 1.0000006 , 1.00000135])

Constrained Optimization

Next, we consider a minimization problem with several constraints. The intial positions for constrained optimization must adhere to the constraints imposed by the problem. This can be ensured using the provided function psopy.init_feasible. Note, there are several caveats regarding the use of this function. Consult its documentation for more information.

>>> # The objective function.
>>> fun = lambda x: (x[0] - 1)**2 + (x[1] - 2.5)**2
>>> # The constraints.
>>> cons = ({'type': 'ineq', 'fun': lambda x:  x[0] - 2 * x[1] + 2},
...         {'type': 'ineq', 'fun': lambda x: -x[0] - 2 * x[1] + 6},
...         {'type': 'ineq', 'fun': lambda x: -x[0] + 2 * x[1] + 2},
...         {'type': 'ineq', 'fun': lambda x: x[0]},
...         {'type': 'ineq', 'fun': lambda x: x[1]})
>>> from psopy import init_feasible
>>> x0 = init_feasible(cons, low=0., high=2., shape=(1000, 2))
>>> res = minimize_pso(fun, x0, constrainsts=cons, options={
...     'g_rate': 1., 'l_rate': 1., 'max_velocity': 4., 'stable_iter': 50})
>>> res.x
array([ 1.39985398,  1.69992748])

Authors

License

Licensed under the BSD 3-Clause License.
Copyright 2018 Abhijit Theophilus, Snehanshu Saha, Suryoday Basak

References

[1]Theophilus, A., Saha, S., Basak, S. and Murthy, J., 2018. A Novel Exoplanetary Habitability Score via Particle Swarm Optimization of CES Production Functions. arXiv preprint arXiv:1805.08858.
[2]Ray, T. and Liew, K.M., 2001. A swarm with an effective information sharing mechanism for unconstrained and constrained single objective optimisation problems. In Evolutionary Computation, 2001. Proceedings of the 2001 Congress on (Vol. 1, pp. 75-80). IEEE.
[3]Eberhart, R. and Kennedy, J., 1995, October. A new optimizer using particle swarm theory. In Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on (pp. 39-43). IEEE.
[4]Shi, Y. and Eberhart, R., 1998, May. A modified particle swarm optimizer. In Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence., The 1998 IEEE International Conference on (pp. 69-73). IEEE.