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Description:

psoa 1.0.1

psoa
An implementation of the Particle Swarm Optimization algorithm
The algorithm can be summarized as follows:

a swarm of moving particles are used to find the extreme value of an objective function
each particle has its own position and velocity

use the given function to evaluate particles' positions
results can be compared, depending on whether we want to maximize or minimize the objective function

In each step, a particle receives three forces, they are used to update the particle's velocity

a friction force that slows down the particle
a random attraction force towards the particle's previous best position
a random attraction force towards the swarm's previous best position

the particle's velocity is then used to update the particle's position
if boundary conditions are included, we consider them to be reflecting boundaries, i.e. if the particle moves beyond the boundary in one direction, we would

place the particle back onto the boundary
and reverse the particle's velocity in that direction

keep updating the particles' positions and velocities until

the swarm's best position converges
or until we reach the preset maximum number of steps

Installation:
pip install psoa

or
conda install -c wangxiangwen psoa

Example Usage:
>>> import psoa
>>> import numpy as np
>>> s = psoa.swarm()
>>> obj = lambda x: -((x[0] - 10) ** 2 + (x[1] - 25) ** 2)
>>> s.maximize(obj, dim=2)
([10.0, 25.0], -0.0)
>>> obj2 = lambda x: np.sum([xi ** 2 - 10 * np.cos(2 * np.pi * xi)
>>> for xi in x]) + 10 * len(x)
>>> s.minimize(obj2, dim=5, max_iteration=1e5,
>>> boundaries=((-5.12, -5.12, -5.12, -5.12, -5.12),
>>> (5.12, 5.12, 5.12, 5.12, 5.12)))
([-2.8743161872992346e-10,
2.579205368330527e-09,
-4.79709591601136e-09,
-1.0974277510973518e-09,
4.4227337040162274e-10],
0.0)