# -*- coding: utf-8 -*-
r"""
A Local-best Particle Swarm Optimization (lbest PSO) algorithm.
Similar to global-best PSO, it takes a set of candidate solutions,
and finds the best solution using a position-velocity update method.
However, it uses a ring topology, thus making the particles
attracted to its corresponding neighborhood.
The position update can be defined as:
.. math::
x_{i}(t+1) = x_{i}(t) + v_{i}(t+1)
Where the position at the current timestep :math:`t` is updated using
the computed velocity at :math:`t+1`. Furthermore, the velocity update
is defined as:
.. math::
v_{ij}(t + 1) = m * v_{ij}(t) + c_{1}r_{1j}(t)[y_{ij}(t) − x_{ij}(t)] + c_{2}r_{2j}(t)[\hat{y}_{j}(t) − x_{ij}(t)]
However, in local-best PSO, a particle doesn't compare itself to the
overall performance of the swarm. Instead, it looks at the performance
of its nearest-neighbours, and compares itself with them. In general,
this kind of topology takes much more time to converge, but has a more
powerful explorative feature.
In this implementation, a neighbor is selected via a k-D tree
imported from :code:`scipy`. Distance are computed with either
the L1 or L2 distance. The nearest-neighbours are then queried from
this k-D tree. They are computed for every iteration.
An example usage is as follows:
.. code-block:: 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, 'k': 3, 'p': 2}
# Call instance of LBestPSO with a neighbour-size of 3 determined by
# the L2 (p=2) distance.
optimizer = ps.single.LocalBestPSO(n_particles=10, dimensions=2,
options=options)
# Perform optimization
stats = optimizer.optimize(fx.sphere, iters=100)
This algorithm was adapted from one of the earlier works of
J. Kennedy and R.C. Eberhart in Particle Swarm Optimization
[IJCNN1995]_ [MHS1995]_
.. [IJCNN1995] J. Kennedy and R.C. Eberhart, "Particle Swarm Optimization,"
Proceedings of the IEEE International Joint Conference on Neural
Networks, 1995, pp. 1942-1948.
.. [MHS1995] J. Kennedy and R.C. Eberhart, "A New Optimizer using Particle
Swarm Theory," in Proceedings of the Sixth International
Symposium on Micromachine and Human Science, 1995, pp. 39–43.
"""
# Import standard library
import logging
# Import modules
import numpy as np
import multiprocessing as mp
from collections import deque
from ..backend.operators import compute_pbest, compute_objective_function
from ..backend.topology import Ring
from ..backend.handlers import BoundaryHandler, VelocityHandler, OptionsHandler
from ..base import SwarmOptimizer
from ..utils.reporter import Reporter
[docs]class LocalBestPSO(SwarmOptimizer):
[docs] def __init__(
self,
n_particles,
dimensions,
options,
bounds=None,
oh_strategy=None,
bh_strategy="periodic",
velocity_clamp=None,
vh_strategy="unmodified",
center=1.00,
ftol=-np.inf,
ftol_iter=1,
init_pos=None,
static=False,
):
"""Initialize the swarm
Attributes
----------
n_particles : int
number of particles in the swarm.
dimensions : int
number of dimensions in the space.
bounds : tuple of numpy.ndarray
a tuple of size 2 where the first entry is the minimum bound
while the second entry is the maximum bound. Each array must
be of shape :code:`(dimensions,)`.
oh_strategy : dict, optional, default=None(constant options)
a dict of update strategies for each option.
bh_strategy : str
a strategy for the handling of out-of-bounds particles.
velocity_clamp : tuple (default is :code:`(0,1)`)
a tuple of size 2 where the first entry is the minimum velocity
and the second entry is the maximum velocity. It
sets the limits for velocity clamping.
vh_strategy : str
a strategy for the handling of the velocity of out-of-bounds particles.
center : list, optional
an array of size :code:`dimensions`
ftol : float
relative error in objective_func(best_pos) acceptable for
convergence. Default is :code:`-np.inf`
ftol_iter : int
number of iterations over which the relative error in
objective_func(best_pos) is acceptable for convergence.
Default is :code:`1`
options : dict with keys :code:`{'c1', 'c2', 'w', 'k', 'p'}`
a dictionary containing the parameters for the specific
optimization technique
* c1 : float
cognitive parameter
* c2 : float
social parameter
* w : float
inertia parameter
* k : int
number of neighbors to be considered. Must be a
positive integer less than :code:`n_particles`
* p: int {1,2}
the Minkowski p-norm to use. 1 is the
sum-of-absolute values (or L1 distance) while 2 is
the Euclidean (or L2) distance.
init_pos : numpy.ndarray, optional
option to explicitly set the particles' initial positions. Set to
:code:`None` if you wish to generate the particles randomly.
static: bool
a boolean that decides whether the Ring topology
used is static or dynamic. Default is `False`
"""
if oh_strategy is None:
oh_strategy = {}
# Initialize logger
self.logger = logging.getLogger(__name__)
# Assign k-neighbors and p-value as attributes
self.k, self.p = options["k"], options["p"]
# Initialize parent class
super(LocalBestPSO, self).__init__(
n_particles=n_particles,
dimensions=dimensions,
options=options,
bounds=bounds,
velocity_clamp=velocity_clamp,
center=center,
ftol=ftol,
ftol_iter=ftol_iter,
init_pos=init_pos,
)
# Initialize logger
self.rep = Reporter(logger=logging.getLogger(__name__))
# Initialize the resettable attributes
self.reset()
# Initialize the topology
self.top = Ring(static=static)
self.bh = BoundaryHandler(strategy=bh_strategy)
self.vh = VelocityHandler(strategy=vh_strategy)
self.oh = OptionsHandler(strategy=oh_strategy)
self.name = __name__
[docs] def optimize(
self, objective_func, iters, n_processes=None, verbose=True, **kwargs
):
"""Optimize the swarm for a number of iterations
Performs the optimization to evaluate the objective
function :code:`f` for a number of iterations :code:`iter.`
Parameters
----------
objective_func : callable
objective function to be evaluated
iters : int
number of iterations
n_processes : int
number of processes to use for parallel particle evaluation (default: None = no parallelization)
verbose : bool
enable or disable the logs and progress bar (default: True = enable logs)
kwargs : dict
arguments for the objective function
Returns
-------
tuple
the local best cost and the local best position among the
swarm.
"""
# Apply verbosity
if verbose:
log_level = logging.INFO
else:
log_level = logging.NOTSET
self.rep.log("Obj. func. args: {}".format(kwargs), lvl=logging.DEBUG)
self.rep.log(
"Optimize for {} iters with {}".format(iters, self.options),
lvl=log_level,
)
# Populate memory of the handlers
self.bh.memory = self.swarm.position
self.vh.memory = self.swarm.position
# Setup Pool of processes for parallel evaluation
pool = None if n_processes is None else mp.Pool(n_processes)
self.swarm.pbest_cost = np.full(self.swarm_size[0], np.inf)
ftol_history = deque(maxlen=self.ftol_iter)
for i in self.rep.pbar(iters, self.name) if verbose else range(iters):
# Compute cost for current position and personal best
self.swarm.current_cost = compute_objective_function(
self.swarm, objective_func, pool=pool, **kwargs
)
self.swarm.pbest_pos, self.swarm.pbest_cost = compute_pbest(
self.swarm
)
best_cost_yet_found = np.min(self.swarm.best_cost)
# Update gbest from neighborhood
self.swarm.best_pos, self.swarm.best_cost = self.top.compute_gbest(
self.swarm, p=self.p, k=self.k
)
if verbose:
self.rep.hook(best_cost=np.min(self.swarm.best_cost))
# Save to history
hist = self.ToHistory(
best_cost=self.swarm.best_cost,
mean_pbest_cost=np.mean(self.swarm.pbest_cost),
mean_neighbor_cost=np.mean(self.swarm.best_cost),
position=self.swarm.position,
velocity=self.swarm.velocity,
)
self._populate_history(hist)
# Verify stop criteria based on the relative acceptable cost ftol
relative_measure = self.ftol * (1 + np.abs(best_cost_yet_found))
delta = (
np.abs(self.swarm.best_cost - best_cost_yet_found)
< relative_measure
)
if i < self.ftol_iter:
ftol_history.append(delta)
else:
ftol_history.append(delta)
if all(ftol_history):
break
# Perform options update
self.swarm.options = self.oh(
self.options, iternow=i, itermax=iters
)
# Perform position velocity update
self.swarm.velocity = self.top.compute_velocity(
self.swarm, self.velocity_clamp, self.vh, self.bounds
)
self.swarm.position = self.top.compute_position(
self.swarm, self.bounds, self.bh
)
# Obtain the final best_cost and the final best_position
final_best_cost = self.swarm.best_cost.copy()
final_best_pos = self.swarm.pbest_pos[
self.swarm.pbest_cost.argmin()
].copy()
# Write report in log and return final cost and position
self.rep.log(
"Optimization finished | best cost: {}, best pos: {}".format(
final_best_cost, final_best_pos
),
lvl=log_level,
)
# Close Pool of Processes
if n_processes is not None:
pool.close()
return (final_best_cost, final_best_pos)