Cross-Entropy Method (CEM)¶
- class pypop7.optimizers.cem.cem.CEM(problem, options)¶
Cross-Entropy Method (CEM).
This is the abstract class for all CEM classes. Please use any of its instantiated subclasses to optimize the black-box problem at hand.
Note
- CEM is a class of principled population-based optimizers, proposed originally by Rubinstein,
whose core idea is based on Kullback–Leibler (or Cross-Entropy) minimization.
- 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’ - number of individuals/samples (int, default: 1000),
’n_parents’ - number of elitists (int, default: 200).
- mean¶
initial (starting) point, aka mean of Gaussian search (mutation/sampling) distribution.
- Type:
array_like
- n_individuals¶
number of individuals/samples.
- Type:
int
- n_parents¶
number of elitists.
- Type:
int
- sigma¶
initial global step-size, aka mutation strength.
- Type:
float
References
Amos, B. and Yarats, D., 2020, November. The differentiable cross-entropy method. In International Conference on Machine Learning (pp. 291-302). PMLR. http://proceedings.mlr.press/v119/amos20a.html
Rubinstein, R.Y. and Kroese, D.P., 2016. Simulation and the Monte Carlo method (Third Edition). John Wiley & Sons. https://onlinelibrary.wiley.com/doi/book/10.1002/9781118631980
Hu, J., Fu, M.C. and Marcus, S.I., 2007. A model reference adaptive search method for global optimization. Operations Research, 55(3), pp.549-568. https://pubsonline.informs.org/doi/abs/10.1287/opre.1060.0367
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
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
Rubinstein, R.Y. and Kroese, D.P., 2004. The cross-entropy method: a unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning. New York: Springer. https://link.springer.com/book/10.1007/978-1-4757-4321-0