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ipso.py
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import numpy as np # engine for numerical computing
from pypop7.optimizers.core.optimizer import Optimizer
from pypop7.optimizers.pso.pso import PSO # abstract class of all particle swarm optimizer (PSO) classes
class IPSO(PSO):
"""Incremental Particle Swarm Optimizer (IPSO).
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`),
* 'constriction' - constriction factor (`float`, default: `0.729`),
* 'cognition' - cognitive learning rate (`float`, default: `2.05`),
* 'society' - social learning rate (`float`, default: `2.05`),
* 'max_ratio_v' - maximal ratio of velocities w.r.t. search range (`float`, default: `0.5`).
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.ipso import IPSO
>>> 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}
>>> ipso = IPSO(problem, options) # initialize the optimizer class
>>> results = ipso.optimize() # run the optimization process
>>> # return the number of function evaluations and best-so-far fitness
>>> print(f"IPSO: {results['n_function_evaluations']}, {results['best_so_far_y']}")
IPSO: 5000, 2.29225104244031e-07
For its correctness checking of coding, refer to `this code-based repeatability report
<https://tinyurl.com/4pk3ssrf>`_ for more details.
Attributes
----------
cognition : `float`
cognitive learning rate, aka acceleration coefficient.
constriction : `float`
constriction factor.
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
----------
De Oca, M.A.M., Stutzle, T., Van den Enden, K. and Dorigo, M., 2011.
Incremental social learning in particle swarms.
IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 41(2), pp.368-384.
https://ieeexplore.ieee.org/document/5582312
"""
def __init__(self, problem, options):
PSO.__init__(self, problem, options)
self.n_individuals = 1 # minimum of swarm size
self.max_n_individuals = options.get('max_n_individuals', 1000) # maximum of swarm size
assert self.max_n_individuals > 0
self.cognition = options.get('cognition', 2.05) # cognitive learning rate
assert self.cognition > 0.0
self.society = options.get('society', 2.05) # social learning rate
assert self.society > 0.0
self.constriction = options.get('constriction', 0.729) # constriction factor
assert self.constriction > 0.0
self.max_ratio_v = options.get('max_ratio_v', 0.5) # maximal ratio of velocity
assert 0.0 <= self.max_ratio_v <= 1.0
def initialize(self, args=None):
v = np.zeros((self.n_individuals, self.ndim_problem)) # velocities
x = self.rng_initialization.uniform(self.initial_lower_boundary, self.initial_upper_boundary,
size=self._swarm_shape) # positions
y = np.empty((self.n_individuals,)) # fitness
p_x, p_y = np.copy(x), np.copy(y) # personally previous-best positions and fitness
for i in range(self.n_individuals):
if self._check_terminations():
return v, x, y, p_x, p_y
y[i] = self._evaluate_fitness(x[i], args)
p_y = np.copy(y)
return v, x, y, p_x, p_y
def iterate(self, v=None, x=None, y=None, p_x=None, p_y=None, args=None, fitness=None):
for i in range(self.n_individuals): # horizontal social learning
if self._check_terminations():
return v, x, y, p_x, p_y
cognition_rand = self.rng_optimization.uniform(size=(self.ndim_problem,))
society_rand = self.rng_optimization.uniform(size=(self.ndim_problem,))
v[i] = self.constriction*(v[i] + self.cognition*cognition_rand*(p_x[i] - x[i]) +
self.society*society_rand*(p_x[np.argmin(p_y)] - x[i])) # velocity update
v[i] = np.clip(v[i], self._min_v, self._max_v)
x[i] += v[i] # position update
x[i] = np.clip(x[i], self.lower_boundary, self.upper_boundary)
y[i] = self._evaluate_fitness(x[i], args)
if y[i] < p_y[i]: # online update
p_x[i], p_y[i] = x[i], y[i]
if self.n_individuals < self.max_n_individuals: # population growth (vertical social learning)
if self._check_terminations():
return v, x, y, p_x, p_y
xx = self.rng_optimization.uniform(self.lower_boundary, self.upper_boundary)
model = p_x[np.argmin(p_y)] # the best particle is used as model
# use different random numbers of different dimensions for diversity (important),
# which is *slightly different* from the original paper but often with better performance
# xx += self.rng_optimization.uniform()*(model - xx) # from the original paper
xx += self.rng_optimization.uniform(size=(self.ndim_problem,))*(model - xx)
xx = np.clip(xx, self.lower_boundary, self.upper_boundary)
yy = self._evaluate_fitness(xx, args)
v = np.vstack((v, np.zeros((self.ndim_problem,))))
x, y = np.vstack((x, xx)), np.hstack((y, yy))
p_x, p_y = np.vstack((p_x, xx)), np.hstack((p_y, yy))
self.n_individuals += 1
self._n_generations += 1
return v, x, y, p_x, p_y
def optimize(self, fitness_function=None, args=None):
fitness = Optimizer.optimize(self, fitness_function)
v, x, y, p_x, p_y = self.initialize(args)
while not self.termination_signal:
self._print_verbose_info(fitness, y)
v, x, y, p_x, p_y = self.iterate(v, x, y, p_x, p_y, args)
return self._collect(fitness, y)