import numpy as np
from pypop7.optimizers.core.optimizer import Optimizer
from pypop7.optimizers.pso.spso import PSO
[docs]class CPSO(PSO):
"""Cooperative Particle Swarm Optimizer (CPSO).
Parameters
----------
problem : dict
problem arguments with the following common settings (`keys`):
* 'fitness_function' - objective function to be **minimized** (`func`),
* 'ndim_problem' - number of dimensionality (`int`),
* 'upper_boundary' - upper boundary of search range (`array_like`),
* 'lower_boundary' - lower boundary of search range (`array_like`).
options : dict
optimizer options with the following common settings (`keys`):
* 'max_function_evaluations' - maximum of function evaluations (`int`, default: `np.Inf`),
* 'max_runtime' - maximal runtime to be allowed (`float`, default: `np.Inf`),
* 'seed_rng' - seed for random number generation needed to be *explicitly* set (`int`);
and with the following particular settings (`keys`):
* 'n_individuals' - swarm (population) size, aka number of particles (`int`, default: `20`),
* 'cognition' - cognitive learning rate (`float`, default: `1.49`),
* 'society' - social learning rate (`float`, default: `1.49`),
* 'max_ratio_v' - maximal ratio of velocities w.r.t. search range (`float`, default: `0.2`).
Examples
--------
Use the optimizer to minimize the well-known test function
`Rosenbrock <http://en.wikipedia.org/wiki/Rosenbrock_function>`_:
.. code-block:: python
:linenos:
>>> import numpy
>>> from pypop7.benchmarks.base_functions import rosenbrock # function to be minimized
>>> from pypop7.optimizers.pso.cpso import CPSO
>>> problem = {'fitness_function': rosenbrock, # define problem arguments
... 'ndim_problem': 2,
... 'lower_boundary': -5*numpy.ones((2,)),
... 'upper_boundary': 5*numpy.ones((2,))}
>>> options = {'max_function_evaluations': 5000, # set optimizer options
... 'seed_rng': 2022}
>>> cpso = CPSO(problem, options) # initialize the optimizer class
>>> results = cpso.optimize() # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"CPSO: {results['n_function_evaluations']}, {results['best_so_far_y']}")
CPSO: 5000, 0.3085868239334274
For its correctness checking of coding, refer to `this code-based repeatability report
<https://tinyurl.com/27nx42rm>`_ for more details.
Attributes
----------
cognition : `float`
cognitive learning rate, aka acceleration coefficient.
max_ratio_v : `float`
maximal ratio of velocities w.r.t. search range.
n_individuals : `int`
swarm (population) size, aka number of particles.
society : `float`
social learning rate, aka acceleration coefficient.
References
----------
Van den Bergh, F. and Engelbrecht, A.P., 2004.
A cooperative approach to particle swarm optimization.
IEEE Transactions on Evolutionary Computation, 8(3), pp.225-239.
https://ieeexplore.ieee.org/document/1304845
"""
def __init__(self, problem, options):
PSO.__init__(self, problem, options)
self.cognition = options.get('cognition', 1.49) # cognitive learning rate
assert self.cognition >= 0.0
self.society = options.get('society', 1.49) # social learning rate
assert self.society >= 0.0
self._max_generations = np.ceil(self.max_function_evaluations/(self.n_individuals*self.ndim_problem))
self._w = 1.0 - (np.arange(self._max_generations) + 1.0)/self._max_generations # from 1.0 to 0.0
def iterate(self, v=None, x=None, y=None, p_x=None, p_y=None, n_x=None, args=None):
fitness = []
for j in range(self.ndim_problem):
if self._check_terminations():
return v, x, y, p_x, p_y, n_x, fitness
cognition_rand = self.rng_optimization.uniform(size=(self.n_individuals, self.ndim_problem))
society_rand = self.rng_optimization.uniform(size=(self.n_individuals, self.ndim_problem))
for i in range(self.n_individuals):
if self._check_terminations():
return v, x, y, p_x, p_y, n_x, fitness
n_x[i, j] = p_x[np.argmin(p_y), j]
v[i, j] = (self._w[min(self._n_generations, len(self._w))]*v[i, j] +
self.cognition*cognition_rand[i, j]*(p_x[i, j] - x[i, j]) +
self.society*society_rand[i, j]*(n_x[i, j] - x[i, j])) # velocity update
v[i, j] = np.clip(v[i, j], self._min_v[j], self._max_v[j])
x[i, j] += v[i, j] # position update
xx = np.copy(self.best_so_far_x)
xx[j] = x[i, j]
y[i] = self._evaluate_fitness(xx, args)
fitness.append(y[i])
if y[i] < p_y[i]: # online update
p_x[i, j], p_y[i] = x[i, j], y[i]
self._n_generations += 1
return v, x, y, p_x, p_y, n_x, fitness
def optimize(self, fitness_function=None, args=None):
fitness = Optimizer.optimize(self, fitness_function)
v, x, y, p_x, p_y, n_x = self.initialize(args)
yy = y # only for printing
while not self.termination_signal:
self._print_verbose_info(fitness, yy)
v, x, y, p_x, p_y, n_x, yy = self.iterate(v, x, y, p_x, p_y, n_x, args)
return self._collect(fitness, yy)