# !/usr/bin/env python
# Created by "Thieu" at 18:08, 19/04/2020 ----------%
# Email: nguyenthieu2102@gmail.com %
# Github: https://github.com/thieu1995 %
# --------------------------------------------------%
import numpy as np
from mealpy.optimizer import Optimizer
[docs]class BaseCEM(Optimizer):
"""
The original version of: Cross-Entropy Method (CEM)
Links:
1. https://github.com/clever-algorithms/CleverAlgorithms
2. https://doi.org/10.1007/s10479-005-5724-z
Hyper-parameters should fine tuned in approximate range to get faster convergen toward the global optimum:
+ n_best (int): N selected solutions as a samples for next evolution
+ alpha (float): weight factor for means and stdevs (normal distribution)
Examples
~~~~~~~~
>>> import numpy as np
>>> from mealpy.probabilistic_based.CEM import BaseCEM
>>>
>>> def fitness_function(solution):
>>> return np.sum(solution**2)
>>>
>>> problem_dict1 = {
>>> "fit_func": fitness_function,
>>> "lb": [-10, -15, -4, -2, -8],
>>> "ub": [10, 15, 12, 8, 20],
>>> "minmax": "min",
>>> "verbose": True,
>>> }
>>>
>>> epoch = 1000
>>> pop_size = 50
>>> n_best = 30
>>> alpha = 0.7
>>> model = BaseCEM(problem_dict1, epoch, pop_size, n_best, alpha)
>>> best_position, best_fitness = model.solve()
>>> print(f"Solution: {best_position}, Fitness: {best_fitness}")
References
~~~~~~~~~~
[1] 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.
"""
def __init__(self, problem, epoch=10000, pop_size=100, n_best=30, alpha=0.7, **kwargs):
"""
Args:
problem (dict): The problem dictionary
epoch (int): maximum number of iterations, default = 10000
pop_size (int): number of population size, default = 100
n_best (int): N selected solutions as a samples for next evolution
alpha (float): weight factor for means and stdevs (normal distribution)
"""
super().__init__(problem, kwargs)
self.nfe_per_epoch = pop_size
self.sort_flag = True
self.epoch = epoch
self.pop_size = pop_size
self.alpha = alpha
self.n_best = n_best
self.means = np.random.uniform(self.problem.lb, self.problem.ub)
self.stdevs = np.abs(self.problem.ub - self.problem.lb)
[docs] def evolve(self, epoch):
"""
The main operations (equations) of algorithm. Inherit from Optimizer class
Args:
epoch (int): The current iteration
"""
## Selected the best samples and update means and stdevs
pop_best = self.pop[:self.n_best]
pos_list = np.array([item[self.ID_POS] for item in pop_best])
means_new = np.mean(pos_list, axis=0)
means_new_repeat = np.repeat(means_new.reshape((1, -1)), self.n_best, axis=0)
stdevs_new = np.mean((pos_list - means_new_repeat) ** 2, axis=0)
self.means = self.alpha * self.means + (1.0 - self.alpha) * means_new
self.stdevs = np.abs(self.alpha * self.stdevs + (1.0 - self.alpha) * stdevs_new)
## Create new population for next generation
pop_new = []
for idx in range(0, self.pop_size):
pos_new = np.random.normal(self.means, self.stdevs)
pop_new.append([self.amend_position(pos_new), None])
pop_new = self.update_fitness_population(pop_new)
self.pop = self.greedy_selection_population(self.pop, pop_new)