Source code for pypop7.optimizers.cem.dscem

import numpy as np  # engine for numerical computing

from pypop7.optimizers.cem.scem import SCEM


[docs]class DSCEM(SCEM): """Dynamic Smoothing Cross-Entropy Method (DSCEM). .. note:: `DSCEM` uses the *dynamic* smoothing strategy to update the *mean* and *std* of Gaussian search (mutation/sampling) distribution in an online fashion. 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`): * 'sigma' - initial global step-size, aka mutation strength (`float`), * 'mean' - initial (starting) point, aka mean of Gaussian search distribution (`array_like`), * if not given, it will draw a random sample from the uniform distribution whose search range is bounded by `problem['lower_boundary']` and `problem['upper_boundary']`. * 'n_individuals' - offspring population size (`int`, default: `1000`), * 'n_parents' - parent population size (`int`, default: `200`), * 'alpha' - smoothing factor of mean of Gaussian search distribution (`float`, default: `0.8`), * 'beta' - smoothing factor of individual step-sizes (`float`, default: `0.7`), * 'q' - decay factor of smoothing individual step-sizes (`float`, default: `5.0`). 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 # engine for numerical computing >>> from pypop7.benchmarks.base_functions import rosenbrock # function to be minimized >>> from pypop7.optimizers.cem.dscem import DSCEM >>> problem = {'fitness_function': rosenbrock, # define problem arguments ... 'ndim_problem': 100, ... 'lower_boundary': -5*numpy.ones((100,)), ... 'upper_boundary': 5*numpy.ones((100,))} >>> options = {'max_function_evaluations': 1000000, # set optimizer options ... 'seed_rng': 2022, ... 'sigma': 0.3} # the global step-size may need to be tuned for better performance >>> dscem = DSCEM(problem, options) # initialize the optimizer class >>> results = dscem.optimize() # run the optimization process >>> # return the number of function evaluations and best-so-far fitness >>> print(f"DSCEM: {results['n_function_evaluations']}, {results['best_so_far_y']}") DSCEM: 1000000, 158.66725776324424 For its correctness checking of coding, refer to `this code-based repeatability report <https://tinyurl.com/43f6kjee>`_ for more details. Attributes ---------- alpha : `float` smoothing factor of mean of Gaussian search distribution. beta : `float` smoothing factor of individual step-sizes. mean : `array_like` initial (starting) point, aka mean of Gaussian search distribution. n_individuals : `int` number of offspring, aka offspring population size. n_parents : `int` number of parents, aka parental population size. q : `float` decay factor of smoothing individual step-sizes. sigma : `float` initial global step-size, aka mutation strength. References ---------- Kroese, D.P., Porotsky, S. and Rubinstein, R.Y., 2006. The cross-entropy method for continuous multi-extremal optimization. Methodology and Computing in Applied Probability, 8(3), pp.383-407. https://link.springer.com/article/10.1007/s11009-006-9753-0 (See [Appendix B Main CE Program] for the official Matlab code.) De Boer, P.T., Kroese, D.P., Mannor, S. and Rubinstein, R.Y., 2005. A tutorial on the cross-entropy method. Annals of Operations Research, 134(1), pp.19-67. https://link.springer.com/article/10.1007/s10479-005-5724-z """ def __init__(self, problem, options): SCEM.__init__(self, problem, options) self.beta = options.get('beta', 0.7) # smoothing factor of individual step-sizes assert 0.0 <= self.beta <= 1.0 self.q = options.get('q', 5.0) # decay factor of smoothing individual step-sizes assert self.q >= 0.0 def initialize(self, is_restart=False): mean = self._initialize_mean(is_restart) x = np.empty((self.n_individuals, self.ndim_problem)) # samples (population) y = np.empty((self.n_individuals,)) # fitness (no evaluation) return mean, x, y def iterate(self, mean=None, x=None, y=None, args=None): for i in range(self.n_individuals): if self._check_terminations(): return x, y x[i] = mean + self._sigmas*self.rng_optimization.standard_normal((self.ndim_problem,)) y[i] = self._evaluate_fitness(x[i], args) return x, y def _update_parameters(self, mean=None, x=None, y=None): xx = x[np.argsort(y)[:self.n_parents]] mean = self.alpha*np.mean(xx, axis=0) + (1.0-self.alpha)*mean b_mod = self.beta - self.beta*np.power(1.0 - 1.0/self._n_generations, self.q) self._sigmas = b_mod*np.std(xx, axis=0) + (1.0 - b_mod)*self._sigmas return mean